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Since discovering the holographic principle, I have stretched my brain as far as I can to understand the nature of our "BEING". This site is an attempt to share, promote, utilize and rationalize these "FACTS".

See Explanation.  Clicking on the picture will download
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Composite Crab

black hole

Mr. S. Hawking thinks he's a 'SUCH' a big shot. He decries us philosophers as having remained in the stone age. Actually most philosphers are so dumbfounded by the leaps in science that have occurred lately, that they are still "sitting astonied"; just as deeply as Ezekiel was when his revelations came to him. Yet, while still in such a state of shock and awe, we bravely press on. What does this all mean? Where can such knowledge take us? Have we the moral perpetude to use it properly? All this and much more, brave traveller, will be revealed here and where-ever the 'more-than-mere-mortal' dare to tread.

Just wanted to take the time to thank you for all your awesome work in astrophysics.You have given us so much! Loved universe in a nutshell, awesome stuff. Me, I am an armchair astronomy enthusiast and par-time philosopher. Short GRB's are what really turn me on! My home-made theory of the holographic principle's 5th dimension somehow interfering has been confirmed as a possibility by some to possibly rationalize the short GRB's.
Any comment would be golden to me. I have some of your lectures on my website (Visitors can find it at this location (URL): ), and do not make $ on it as per your request, unless someone would bet ME a pound that you won't write back.               with deep respect
                                    Mike Milne
From: "Professor Hawking" <
Your email regarding "thanks" has been received.
Professor Hawking very much regrets that due to the severe limitations
he works under, and the huge amount of mail he receives, he may not have
time to write you a reply.  All e-mail is read.  We have NO facilities
in our department to deal with specific scientific enquiries, or theories. Please see the website for more informationabout Professor Hawking, his life and his work. Yours faithfully David Pond Graduate Assistant toProfessor S W Hawking CH CBE FRS Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, CB3 0WA.United Kingdom.


press here for

The USS Enterprise NCC-1701-E, from films 8-10 Quotes by Steve...radiation came only in packets or quanta of a certain size....reality might be known to God, but the quantum nature of light would prevent us seeing it...even God is bound by the Uncertainty Principle, and can not know both the position, and the speed, of a particle. So God does play dice with the universe. All the evidence points to him being an inveterate gambler, who throws the dice on every possible occasion....quantum mechanics, was put forward by Heisenberg, the Austrian, Erwin Schroedinger, and the British physicist, Paul Dirac. Dirac was my predecessor but one, as the Lucasian Professor in Cambridge. Although quantum mechanics has been around for nearly 70 years, it is still not generally understood or appreciated, even by those that use it to do calculations. Yet it should concern us all, because it is a completely different picture of the physical universe, and of reality itself. In quantum mechanics, particles don't have well defined positions and speeds. Instead, they are represented by what is called a wave function. This is a number at each point of space. The size of the wave function gives the probability that the particle will be found in that position. The rate, at which the wave function varies from point to point, gives the speed of the particle. One can have a wave function that is very strongly peaked in a small region. This will mean that the uncertainty in the position is small. But the wave function will vary very rapidly near the peak, up on one side, and down on the other. Thus the uncertainty in the speed will be large. 
The USS Enterprise NCC-1701-E, from films 8-10
The Enterprise boldly going where no man had gone before. With more than just hope lets urge
 international consenus on space policy. NASA in all its responsibility must not be the sole decision making voice. Otherwise we end up repeating the history of endless ages of raiding and pillaging other environments that may hold even deeper cosequences than the mess we have made of Mother Earth!


If you had said we would get this stuff just 20 years ago, people would have laughed at you. It is with this realization that I ask you to proceed.


The Holographic Principle

There is strong evidence that the area of any surface limits the information content of adjacent spacetime regions, at 10^(69) bits per square meter. We review the developments that have led to the recognition of this entropy bound, placing special emphasis on the quantum properties of black holes. The construction of light-sheets, which associate relevant spacetime regions to any given surface, is discussed in detail. We explain how the bound is tested and demonstrate its validity in a wide range of examples.
A universal relation between geometry and information is thus uncovered. It has yet to be explained. The holographic principle asserts that its origin must lie in the number of fundamental degrees of freedom involved in a unified description of spacetime and matter. It must be manifest in an underlying quantum theory of gravity. We survey some successes and challenges in implementing the holographic principle.

The Holographic Principle
According to the Holographic Principle, the most information you can get from this image is about 3 x 1065 bits for a normal sized computer monitor. The Holographic Principle, yet unproven, states that there is a maximum amount of information content held by regions adjacent to any surface. Therefore, counter-intuitively, the information content inside a room depends not on the volume of the room but on the area of the bounding walls. The principle derives from the idea that the Planck length, the length scale where quantum mechanics begins to dominate classical gravity, is one side of an area that can hold only about one bit of information. The limit was first postulated by physicist Gerard 't Hooft in 1993. It can arise from generalizations from seemingly distant speculation that the information held by a black hole is determined not by its enclosed volume but by the surface area of its event horizon.
people looking at the above image may not claim to see 3 x 1065 bits, they might claim to see a teapot.
 we owe a lot to you o hubble...happy 15th a jet traveling only 98 percent of light speed rams and mixes with interstellar material. Even higher energy jets might well explain the structure seen around Cygnus A.
 a supermassive black hole in the center of distant galaxy M84 - based on data recently recorded by Hubble's new Space Telescope Imaging Spectrograph (STIS). Very near black holes the force of gravity is so strong that even light can not escape ... but the presence of a black hole can also be revealed by watching matter fall into it. In fact, material spiraling into a black hole would find its speed increasing at a drastic rate. These extreme velocity increases provide a "signature" of the black hole's presence. STIS relies on the Doppler effect to measure gas velocity rapidly increasing to nearly 240 miles per second within 26 light years of the center of M84, a galaxy in the Virgo Cluster about 50 million light years away. The STIS data show that radiation from approaching gas, shifted to blue wavelengths left of the centerline, is suddenly redshifted to the right of center indicating a rapidly rotating disk of material near the galactic nucleus. The resulting sharp S-shape is effectively the signature of a black hole estimated to contain at least 300 million solar masses.
Gamma-Ray Bursting

The Universe in a Nutshell by Stephen Hawking

Stephen Hawking - science's first rock star - returns with a new journey into what makes the world tick, and this time he is determined not to be called again "the most sold and least read" popular science writer, title earned with the publication of A Brief History of Time.In this new book Hawking takes us to the cutting edge of theoretical physics, where truth is often stranger than fiction, to explain in laymen’s terms the principles that control our universe. The book is a fascinating collection of ideas, concepts, principles and connections. ranging from Quantum mechanics to M-theory, from General relativity to11-dimensional supergravity up to 10-dimensional membranes, Superstrings, P-branes and Black holes!One of the most influential thinkers of our time, Stephen Hawking is an intellectual icon, known not only for the adventurousness of his ideas but for the clarity and wit with which he expresses them.

Like many in the community of theoretical physicists, Professor Hawking is seeking to uncover the grail of science — the elusive Theory of Everything that lies at the heart of the cosmos. In his accessible and often playful style, he guides us on his search to uncover the secrets of the universe — from supergravity to supersymmetry, from quantum theory to M-theory, from holography to duality. He takes us to the wild frontiers of science, where superstring theory and p-branes may hold the final clue to the puzzle. And he lets us behind the scenes of one of his most exciting intellectual adventures as he seeks “to combine Einstein’s General Theory of Relativity and Richard Feynman’s idea of multiple histories into one complete unified theory that will describe everything that happens in the universe.” With characteristic exuberance, Professor Hawking invites us to be fellow travelers on this extraordinary voyage through space-time. Copious four-color illustrations help clarify this journey into a surreal wonderland where particles, sheets, and strings move in eleven dimensions; where black holes evaporate and disappear, taking their secret with them; and where the original cosmic seed from which our own universe sprang was a tiny nut. Hawking admits that many of the ideas in the book are highly speculative. In fact, he revels in his role as a provocateur, recollecting with relish the time when he and Kip Thorne pursued the "politically incorrect" idea of time travel. On the subject of M-theory, Hawking acknowledges that extra dimensions are not required to explain any observation. Like other theorists, he is guided by the elegance of the mathematics and by "dualities" indicating that we may already have the fragments of a final theory that will unify gravity and quantum physics. Hawking's book is exciting and provocative, and it poses a fundamental question: Is nature baroque or parsimonious? In the democracy of branes, all dimensions are created equal. From the quantum state of the Big Bang, a cornucopia of universes might emerge. Hawking wields the anthropic principle like Occam's razor to slice through these possibilities. He imagines that life can exist only in a universe with three spatial dimensions, and that an inflated and nearly smooth universe is needed for observers to evolve. In his words, "the anthropic principle picks out brane models from the vast zoo of universes allowed by M-theory." In epistemological circles, the anthropic principle is suspect due to its lack of predictive power and its tendency toward tautology. In the freewheeling world of Stephen Hawking, it is just one more device to tease and engage the reader.Physics Today cover "Toward simulating confined plasmas"  In a magnetically confined plasma, magnetic field lines, such as those depicted in gray, form closed surfaces. An example is the hot-plasma surface shown in red. In this simulation, the surface is tilted a bit off center, which indicates the onset of an instability. To see how the instability progresses and to learn about worldwide efforts to achieve plasma simulations that integrate physics at widely separated time and space scales.

Brief Hisory of time Stephen Hawking : "I want shorter, better focused, numbered questions, not a stream of consciousness." is by his condition allowed to be curt. But if his success tells us anything, it is the folly of reading him solely through his condition. His tone might as easily be a sign of geekiness or superiority or intolerance of non-scientists. Hawking sits in the middle of the room attended by a nurse, one of the 10 who look after him. A PhD student pops his head around the door and says hi - Hawking supervises a small number in his capacity as the Lucasian professor of mathematics, a position once held by Isaac Newton - and the cosmologist either smiles or gears up to communicate. A Brief History of Time, aroused a great deal of interest, but many found it difficult to understand. I decided to write a new version that would be easier to follow. I took the opportunity to add material about new developments and I left out some things of a more technical natureI would hope that people who have difficulty with A Brief History will try a Briefer History and be pleasantly surprised." A Briefer History of Time is not exactly String Theory for Dummies. Like a lot of specialists, Hawking has trouble imagining what it might be like not to understand what he does, or rather, where the non-scientist's understanding will be weak and where strong. The book's range is therefore a little eccentric, lurching between explaining what a scientific theory is ("a model of the universe") and going into quantum mechanics in the kind of vertiginous detail that makes you open your eyes very wide as you read. It is fascinating, up to a point. I put a lot of effort into writing A Briefer History at a time when I was critically ill with pneumonia because I think that it's important for scientists to explain their work, particularly in cosmology. This now answers many questions once asked of religion." There are new sections: string theory - the unproven idea that the universe is made up of lots of tiny, vibrating strings - has apparently moved on since the first book was written, although it is still controversial. This suits Hawking's purpose: he understands that no one, scientist or otherwise, can resist an unanswerable question. When he refers to God it is, as he puts it, in the "impersonal sense", rather as Einstein referred to the laws of nature. It is a euphemism and also a smart bit of marketing, anchoring the unsexy, techie bones of his subject - he once said the best hope for a theory of everything was n=8 supergravity - with the philosophical questions everyone likes to have a stab at.Evolution has ensured that our brains just aren't equipped to visualise 11 dimensions directly. However, from a purely mathematical point of view it's just as easy to think in 11 dimensions, as it is to think in three or four."yet he is working on a children's book about relativity with his daughter Lucy, because children are the best audience: "Naturally interested in space and not afraid to ask why."It is a waste of time to be angry about my disability. One has to get on with life and I haven't done badly. People won't have time for you if you are always angry or complaining."There are pictures of Marilyn Monroe on the wall, one of which has been digitally manipulated to feature Hawking in the foreground. I see a card printed with the slogan: Yes, I am the centre of the universe.  At first sight, it seems remarkable that the universe is so finely tuned. Maybe this is evidence, that the universe was specially designed to produce the human race. However, one has to be careful about such arguments, because of what is known as the Anthropic Principle. This is based on the self-evident truth, that if the universe had not been suitable for life, we wouldn’t be asking why it is so finely adjusted. One can apply the Anthropic Principle, in either its Strong, or Weak, versions. For the Strong Anthropic Principle, one supposes that there are many different universes, each with different values of the physical constants. In a small number, the values will allow the existence of objects like carbon atoms, which can act as the building blocks of living systems. Since we must live in one of these universes, we should not be surprised that the physical constants are finely tuned. If they weren’t, we wouldn’t be here. The strong form of the Anthropic Principle is not very satisfactory. What operational meaning can one give to the existence of all those other universes? And if they are separate from our own universe, how can what happens in them, affect our universe. Instead, I shall adopt what is known as the Weak Anthropic Principle.... It took a very long time, two and a half billion years, to go from single cells to multi-cell beings, which are a necessary precursor to intelligence. This is a good fraction of the total time available, before the Sun blows up. So it would be consistent with the hypothesis, that the probability for life to develop intelligence, is low. In this case, we might expect to find many other life forms in the galaxy, but we are unlikely to find intelligent life. There used to be a project called SETI, the search for extra-terrestrial intelligence. It involved scanning the radio frequencies, to see if we could pick up signals from alien civilisations. I thought this project was worth supporting, though it was cancelled due to a lack of funds. But we should have been wary of answering back, until we have develop a bit further. Meeting a more advanced civilisation, at our present stage, might be a bit like the original inhabitants of America meeting Columbus. I don’t think they were better off for it.'life' is based on chains of carbon atoms, with a few other atoms, such as nitrogen or phosphorous. One can speculate that one might have life with some other chemical basis, such as silicon, but carbon seems the most favourable case, because it has the richest chemistry. That carbon atoms should exist at all, with the properties that they have, requires a fine adjustment of physical constants, such as the QCD scale, the electric charge, and even the dimension of space-time. If these constants had significantly different values, either the nucleus of the carbon atom would not be stable, or the electrons would collapse in on the nucleus. At first sight, it seems remarkable that the universe is so finely tuned. Maybe this is evidence, that the universe was specially designed to produce the human race.

Anatomy of a Black Hole

By definition a black hole is a region where matter collapses to infinite density, and where, as a result, the curvature of spacetime is extreme. Moreover, the intense gravitational field of the black hole prevents any light or other electromagnetic radiation from escaping. But where lies the "point of no return" at which any matter or energy is doomed to disappear from the visible universe?

The Event Horizon

Applying the Einstein Field Equations to collapsing stars, German astrophysicist Kurt Schwarzschild deduced the critical radius for a given mass at which matter would collapse into an infinitely dense state known as a singularity. For a black hole whose mass equals 10 suns, this radius is about 30 kilometers or 19 miles, which translates into a critical circumference of 189 kilometers or 118 miles.

Schwarzschild Black Hole

If you envision the simplest three-dimensional geometry for a black hole, that is a sphere (known as a Schwarzschild black hole), the black hole's surface is known as the event horizon. Behind this horizon, the inward pull of gravity is overwhelming and no information about the black hole's interior can escape to the outer universe.

Apparent versus Event Horizon

As a doomed star reaches its critical circumference, an "apparent" event horizon forms suddenly. Why "apparent?" Because it separates light rays that are trapped inside a black hole from those that can move away from it. However, some light rays that are moving away at a given instant of time may find themselves trapped later if more matter or energy falls into the black hole, increasing its gravitational pull. The event horizon is traced out by "critical" light rays that will never escape or fall in.

Apparent versus Event Horizon


Even before the star meets its final doom, the event horizon forms at the center, balloons out and breaks through the star's surface at the very moment it shrinks through the critical circumference. At this point in time, the apparent and event horizons merge as one: the horizon. For more details, see the caption for the above diagram.

The distinction between apparent horizon and event horizon may seem subtle, even obscure. Nevertheless the difference becomes important in computer simulations of how black holes form and evolve.

Beyond the event horizon, nothing, not even light, can escape. So the event horizon acts as a kind of "surface" or "skin" beyond which we can venture but cannot see. Imagine what happens as you approach the horizon, then cross the threshold.

Care to take a one-way trip into a black hole?

The Singularity

At the center of a black hole lies the singularity, where matter is crushed to infinite density, the pull of gravity is infinitely strong, and spacetime has infinite curvature. Here it's no longer meaningful to speak of space and time, much less spacetime. Jumbled up at the singularity, space and time cease to exist as we know them.

The Limits of Physical Law

Newton and Einstein may have looked at the universe very differently, but they would have agreed on one thing: all physical laws are inherently bound up with a coherent fabric of space and time.

At the singularity, though, the laws of physics, including General Relativity, break down. Enter the strange world of quantum gravity. In this bizzare realm in which space and time are broken apart, cause and effect cannot be unraveled. Even today, there is no satisfactory theory for what happens at and beyond the singularity.

Cosmic Censorship

It's no surprise that throughout his life Einstein rejected the possibility of singularities. So disturbing were the implications that, by the late 1960s, physicists conjectured that the universe forbade "naked singularities." After all, if a singularity were "naked," it could alter the whole universe unpredictably. All singularities within the universe must therefore be "clothed."

But inside what? The event horizon, of course! Cosmic censorship is thus enforced. Not so, however, for that ultimate cosmic singularity that gave rise to the Big Bang.

Science versus Speculation

We can't see beyond the event horizon. At the singularity, randomness reigns supreme. What, then, can we really "know" about black holes? How can we probe their secrets? The answer in part lies in understanding their evolution right after they form

Physics Colloquiums

Rotation, Nut charge and Anti de Sitter space
This lecture is the intellectual property of Professor S.W. Hawking. You may not reproduce, edit or distribute this document in anyway for monetary advantage. The work I'm going to talk about has been carried out with Chris Hunter and Marika Taylor Robinson at Cambridge, and Don Page at Alberta.References It is described in the first three papers shown on the screen. Related work has been carried out by Chamblin, Emparan, Johnson, and Myers. However, they seemed a bit uncertain what reference background to use. I have also shown a reference to Dowker which is relevant.
It has been known for quite a time, that black holes behave like they have entropy. The entropy is the area of the horizon, divided by 4 G, where G is Newton's constant. Black Hole Entropy
The idea is that the Euclidean sections of black hole metrics are periodic in the imaginary time coordinate. Thus they represent black holes in equilibrium with thermal radiation. However there are problems with this interpretation.Problems with thermodynamic interpretation
(first problem appear)
First, one can not have thermal radiation in asymptotically flat space, all the way to infinity, because the energy density would curve the space, and make it an expanding or collapsing Friedmann universe. Thus, if you want a static situation, you have to resort to the dubious Gedanken experiment, of putting the black hole in a box. But you don't find black hole proof boxes, advertised on the Internet.
(second problem appear)
The second difficulty with black holes in equilibrium with thermal radiation is that black holes have negative specific heat. In many cases, when they absorb energy, they get larger and colder. This reduces the radiation they give off, and so they absorb faster than they radiate, and the equilibrium is unstable. This is closely related to the fact that the Euclidean metric has a negative mode. Thus it seems that asymptotically flat Euclidean black holes, describe the decay of hot flat space, rather than a black hole in equilibrium with thermal radiation.
(third problem appear)
The third difficulty with the idea of equilibrium is that if the black hole is rotating, the thermal radiation should be co-rotating with it. But far away from the black hole, the radiation would be co-rotating faster than light, which is impossible. Thus, again one has to use the artificial expedient, of a box of finite size.
Way back in pre-history, Don page and I, realized one could avoid the first two difficulties, if one considered black holes in anti de Sitter space, rather than asymptotically-flat space. In anti de Sitter space, the gravitational potential increases as one goes to infinity. This red shifts the thermal radiation, and means that it has finite energy. Thus anti de Sitter space can exist at finite temperature, without collapsing. In a sense, the gravitational potential in anti de Sitter space, acts like a confining box.
Anti de Sitter space can also help with the second problem, that the equilibrium between black holes and thermal radiation, will be unstable. Small black holes in anti de Sitter space, have negative specific heat, like in asymptotically flat space, and are unstable. But black holes larger than the curvature radius of anti de Sitter space, have positive specific heat, and are presumably stable. At the time, Don page and I, did not think about rotating black holes. But I recently came back to the problem, along with Chris Hunter, and Marika Taylor Robinson. We realized that thermal radiation in anti de Sitter space could co-rotate with up to some limiting angular velocity, without having to travel faster than light. Thus anti de Sitter boundary conditions, can solve all three problems, in the interpretation of Euclidean black holes, as equilibria of black holes, with thermal radiation. Anti de Sitter black holes may not seem of much interest, because we can be fairly sure, that the universe is not asymptotically anti de Sitter. However, they seem worth studying, both for the reasons I have just given, and because of the Maldacena conjecture, relating asymptotically anti de Sitter spaces, to conformal field theories on their boundary. I shall report on two pieces of work in relation to this conjecture. One is a study of rotating black holes in anti de Sitter space. We have found Kerr anti de Sitter metrics in four and five dimensions. As they approach the critical angular velocity in anti de Sitter space, their entropy, as measured by the horizon area, diverges. We compare this entropy, with that of a conformal field theory on the boundary of anti de Sitter space. This also diverges at the critical angular velocity, when the rotational velocity, approaches the speed of light. We show that the two divergences are similar.
The other piece of work, is a study of gravitational entropy, in a more general setting. The quarter area law, holds for black holes or black branes in any dimension, d, that have a horizon, which is a d minus 2 dimensional fixed point set, of a U1 isometry group. However Chris Hunter and I, have recently shown that entropy can be associated with a more general class of space-times. In these, the U1 isometry group can have fixed points on surfaces of any even co-dimension, and the space-time need not be asymptotically flat, or asymptotically anti de Sitter. In these more general class, the entropy is not just a quarter the area, of the d minus two fixed point set. Among the more general class of space-times for which entropy can be defined, an interesting case is those with Nut charge. Nut charge can be defined in four dimensions, and can be regarded as a magnetic type of mass. Solutions with nut charge are not asymptotically flat in the usual sense. Instead, they are said to be asymptotically locally flat, or ALF. In the Euclidean regime, in which I shall be working, the difference can be described as follows. An asymptotically flat metric, like Euclidean Schwarzschild, has a boundary at infinity, that is a two-sphere of radius r, cross a circle, whose radius is asymptotically constant.
To get finite values for the action and Hamiltonian, one subtracts the values for flat space, periodically identified. In asymptotically locally flat metrics, on the other hand, the boundary at infinity, is an S1 bundle over S2. These bundles are labeled by their first Chern number, which is proportional to the Nut charge. If the first Chern number is zero, the boundary is the product, S2 cross S1, and the metric is asymptotically flat. However, if the first Chern number is k, the boundary is a squashed three sphere, with mod k points identified around the S1 fibers. Such asymptotically locally flat metrics, can not be matched to flat space at infinity, to give a finite action and Hamiltonian, despite a number of papers that claim it can be done. The best that one can do, is match to the self-dual multi Taub nut solutions. These can be regarded as defining the vacuums for ALF metrics.
In the self-dual Taub Nut solution, the U1 isometry group, has a zero dimensional fixed point set at the center, called a nut. However, the same ALF boundary conditions, admit another Euclidean solution, called the Taub bolt metric, in which the nut is replaced by a two dimensional bolt. The interesting feature, is that according to the new definition of entropy, the entropy of Taub bolt, is not equal to a quarter the area of the bolt, in Planck units. The reason is that there is a contribution to the entropy from the Misner string, the gravitational counterpart to a Dirac string for a gauge field. The fact that black hole entropy is proportional to the area of the horizon has led people to try and identify the microstates, with states on the horizon. After years of failure, success seemed to come in 1996, with the paper of Strominger and Vafa, which connected the entropy of certain black holes, with a system of D-branes. With hindsight, this can now be seen as an example of a duality, between a gravitational theory in asymptotically anti de Sitter space, and a conformal field theory on its boundary.
It would be interesting if similar dualities could be found for solutions with Nut charge, so that one could verify that the contribution of the Misner string was reflected in the entropy of a conformal field theory. This would be particularly significant for solutions like Taub bolt, which don't have a spin structure. It would show whether the duality between anti de Sitter space, and conformal field theories on its boundary, depends on super symmetry. In fact, I will present evidence, that the duality requires super symmetry.
To investigate the effect of Nut charge, we have found a family of Taub bolt anti de Sitter solutions. These Euclidean metrics are characterized by an integer, k, and a positive parameter, s. The boundary at large distances is an S1 bundle over S2, with first Chern number, k. If k=0, the boundary is a product, S1 cross S2, and the space is asymptotically anti de Sitter, in the usual sense. But if k is not zero, they are what may be called, asymptotically locally anti de Sitter, or ALADS. The boundary is a squashed three sphere, with k points identified around the U1 direction. This is just like asymptotically locally flat, or ALF metrics. But unlike the ALF case, the squashing of the three-sphere, tends to a finite limit, as one approaches infinity. This means that the boundary has a well-defined conformal structure. One can then ask whether the partition function and entropy, of a conformal field theory on the boundary, is related to the action and entropy, of these asymptotically locally anti de Sitter solutions.
To make the ADS, CFT correspondence well posed, we have to specify the reference backgrounds, with respect to which the actions and Hamiltonians are defined. For Kerr anti de Sitter, the reference background is just identified anti de Sitter space. However, as in the asymptotically locally flat case, a squashed three sphere, can not be imbedded in Euclidean anti de Sitter. One therefore can not use it as a reference background, to make the action and Hamiltonian finite. Instead, one has to use Taub Nut anti de Sitter, which is a limiting case of our family. If mod k is greater than one, there is an orbifold singularity in the reference backgrounds, but not in the Taub bolt anti de Sitter solutions. These orbifold singularities in the backgrounds could be resolved, by replacing a small neighbourhood of the nut, by an ALE metric. We shall take it, that the orbifold singularities are harmless.
Another issue that has to be resolved, is what conformal field theory to use, on the boundary of the anti de Sitter space. For five dimensional Kerr anti de Sitter space, there are good reasons to believe the boundary theory is large N Yang Mills. But for four-dimensional Kerr anti de Sitter, or Taub bolt anti de Sitter, we are on shakier ground. On the three dimensional boundaries of four dimensional anti de Sitter spaces, Yang Mills theory is not conformally invariant. The folklore is that one takes the infrared fixed point, of three-dimensional Yang Mills, but no one knows what this is. The best we can do, is calculate the determinants of free fields on the squashed three sphere, and see if they have the same dependence on the squashing, as the action. Note that as the boundary is odd dimensional, there is no conformal anomaly. The determinant of a conformally invariant operator, will just be a function of the squashing. We can then interpret the squashing, as the inverse temperature, and get the number of degrees of freedom, from a comparison with the entropy of ordinary black holes, in four dimensional anti de Sitter. I now turn to the question, of how one can define the entropy, of a space-time. A thermodynamic ensemble, is a collection of systems, whose charges are constrained by La-grange multipliers.
Partition functionOne such charge, is the energy or mass, with the Lagrange multiplier being the inverse temperature, beta. But one can also constrain the angular momentum, and gauge charges. The partition function for the ensemble, is the sum over all states, of e to the minus, La-grange multipliers, times associated charges.
Thus it can be written as, trace of e to the minus Q. Here Q is the operator that generates a Euclidean time translation, beta, a rotation, delta phi, and a gauge transformation, alpha. In other words, Q is the Hamiltonian operator, for a lapse that is beta at infinity, and a shift that is a rotation through delta phi. This means that the partition function can be represented by a Euclidean path integral.
The path integral is over all metrics which at infinity, are periodic under the combination of a Euclidean time translation, beta, a rotation through delta phi, and a gauge rotation, alpha. The lowest order contributions to the path integral for the partition function will come from Euclidean solutions with a U1 isometry, that agree with the periodic boundary conditions at infinity. The Hamiltonian in general relativity or supergravity, can be written as a volume integral over a surface of constant tau, plus surface integrals over its boundaries. Gravitational Hamiltonian The volume integral vanishes by the constraint equations. Thus the numerical value of the Hamiltonian, comes entirely from the surface terms. The action can be related to the Hamiltonian in the usual way. Because the metric has a time translation isometry, all dotted quantities vanish. Thus the action is just beta times the Hamiltonian.If the solution can be foliated by a family of surfaces, that agree with Euclidean time at infinity, the only surface terms will be at infinity.
Family of time surfaces In this case, a solution can be identified under any time translation, rotation, or gauge transformation at infinity. This means that the action will be linear in beta, delta phi, and alpha. If one takes such a linear action, for the partition function, and applies the standard thermodynamic relations, one finds the entropy is zero.The situation is very different however, if the solution can't be foliated by surfaces of constant tau, where tau is the parameter of the U1 isometry group, which agrees with the periodic identification at infinity. Breakdown of foliation The break down of foliation can occur in two ways. The first is at fixed points of the U1 isometry group. These occur on surfaces of even co-dimension. Fixed-point sets of co-dimension-two play a special role. I shall refer to them as bolts. Examples include the horizons of non-extreme black holes and p-branes, but there can be more complicated cases, like Taub bolt.
The other way the foliation by surfaces of constant tau, can break down, is if there are what are called, Misner strings. Kaluza Klein metricTo explain what they are, write the metric in the Kaluza Klein form, with respect to the U1 isometry group. The one form, omega, the scalar, V, and the metric, gamma, can be regarded as fields on B, the space of orbits of the isometry group.
If B has homology in dimension two, the Kaluza Klein field strength, F, can have non-zero integrals over two cycles. This means that the one form, omega, will have Dirac strings in B. In turn, this will mean that the foliation of the spacetime, M, by surfaces of constant tau, will break down on surfaces of co-dimension two, called Misner strings. In order to do a Hamiltonian treatment using surfaces of constant tau, one has to cut out small neighbourhoods of the fixed point sets, and the Misner strings. This modifies the treatment, in two ways. First, the surfaces of constant tau now have boundaries at the fixed-point sets, and Misner strings, as well as the boundary at infinity. This means there can be additional surface terms in the Hamiltonian. In fact, the surface terms at the fixed-point sets are zero, because the shift and lapse vanish there. On the other hand, at a Misner string, the lapse vanishes, but the shift is non zero. The Hamiltonian can therefore have a surface term on the Misner string, which is the shift, times a component of the second fundamental form, of the constant tau surfaces. The total Hamiltonian, will be the sum of this Misner string Hamiltonian, and the Hamiltonian surface term at infinity. Consequences of non-foliation
As before, the action will be beta times the Hamiltonian. However, this will be the action of the space-time, with the neighborhoods of the fixed-point sets and Misner strings removed. To get the action of the full space-time, one has to put back the neighborhoods. When one does so, the surface term associated with the Einstein Hilbert action, will give a contribution to the action, of minus area over 4G, for the bolts and Misner strings. Here G is Newton's constant in the dimension one is considering. The surface terms around lower dimensional fixed-point sets make no contribution to the action. The action of the space-time, will be the lowest order contribution to minus log Z, where Z is the partition function. But log Z is equal to the entropy, minus beta times the Hamiltonian at infinity. So the entropy is a quarter the area of the bolts and Misner strings, minus beta times the Hamiltonian on the Misner strings. In other words, the entropy is the amount by which the action is less than the value, beta times the Hamiltonian at infinity, that it would have if the surfaces of constant tau, foliated the space-time.
This formula for the entropy applies in any dimension and for any class of boundary condition at infinity. Thus one can use it for rotating black holes, in anti de Sitter space. In this case, the reference background is just Euclidean anti de Sitter space, identified with imaginary time period, beta, and appropriate rotation.

Four-dimensional Kerr-AdS
The four-dimensional Kerr anti de Sitter solution, was found by Carter, and is shown on the slide. The parameter, a, determines the rate of rotation. When a-l approaches 1, the co-rotation velocity approaches the speed of light at infinity. It is therefore interesting to examine the behavior of the black hole action, and the conformal field theory partition function, in this limit.
To calculate the action of the black hole is quite delicate, because one has to match it to rotating anti de Sitter space, and subtract one infinite quantity, from another.

Euclidean action.
Nevertheless, this can be done in a well-defined way, and the result is shown on the slide. As you might expect, it diverges at the critical angular velocity, at which the co-rotating velocity, approaches the speed of light.The boundary of rotating anti de Sitter, is a rotating Einstein universe, of one dimension lower. Thus it is straightforward in principle, to calculate the partition function for a free conformal field on the boundary. Someone like Dowker might have calculated the result exactly. However, as we are only human, we looked only at the divergence in the partition function, as one approaches the critical angular velocity.
This divergence arises because in the mode sum for the partition function, one has Bose-Einstein factors with a correction because of the rotation. As one approaches the critical angular velocity, this causes a Bose-Einstein condensation in modes with the maximum axial quantum number, m.
Conformal field theory The divergence in the conformal field theory partition function has the same divergence as the black hole action, at the critical angular velocity. I haven't compared the residues. This is difficult, because it is not clear what three-dimensional conformal field theory one should use on the boundary of four dimensional anti de Sitter. Five-dimensional Kerr-AdS The case of rotating black holes in anti de Sitter five, is broadly similar, but with some differences. One of these is that, because the spatial rotation group, O4, is of rank 2, there are two rotation parameters, a & b. Each of these must have absolute value less than l to the minus one, for the co-rotation velocity to be less than the speed of light, all the way out to infinity. If just one of a & b, approaches the limiting value, the action of the black hole, and the partition function of the conformal field theory, both diverge in a manner similar to the four dimensional case. Action of five-dimensional Kerr-AdS But if a = b, and they approach the limit together, the action and the partition function, both have the same stronger divergence. Again, I haven't compared residues, but this might be worth doing. It may be that in the critical angular velocity limit, the interactions between the particles of super Yang Mills theory, become unimportant. If this is the case, one would expect the action and partition function to agree, rather than differ by a factor of four thirds, as in the non rotating case. Asymptotically locally flat I now turn the case of Nut charge. For asymptotically locally flat metrics in four dimensions, the reference background is the self-dual Taub Nut solution. The Taub bolt solution, has the same asymptotic behavior, but with the zero-dimensional nut fixed point, replaced by a two-dimensional bolt. The area of the bolt is 12 pi N squared, where N is the Nut charge. The area of the Misner string is minus 6 pi N squared. That is to say, the area of the Misner string in Taub bolt, is infinite, but it is less than the area of the Misner string in Taub nut, in a well-defined sense. The Hamiltonian on the Misner string, is N over 8. Again the Misner string Hamiltonian is infinite, but the difference from Taub nut, is finite. And the period, beta, is 8pi N. Thus the entropy, is pi N squared. Note that this is less than a quarter the area of the bolt, which would give 3 pi N squared. It is the effect of the Misner string that reduces the entropy. Taub Nut Anti de Sitter We would like to confirm the effect of Misner strings on entropy, by seeing what effect they have on conformal field theories, on the boundary of anti de Sitter space. For this purpose we constructed versions of Taub nut and Taub bolt, with a negative cosmological constant. The Taub nut anti de Sitter metric is shown on the transparancy. The parameter E, is the squashing of the three-sphere at infinity. If E=1, the three spheres are round, and the metric is Euclidean anti de Sitter space. However, if E is not equal to one, the metric can not be matched to anti de Sitter space at large distance. Each value of E, therefore, defines a different sector of ALADS metrics. This is an important point, which did not seem to have been realized by Chamblin et al. Taub Bolt Anti de Sitter One can also find a family of Taub bolt anti de Sitter metrics, with the same asymptotic behavior. These are characterized by an integer, k, and a positive quantity, s. These determine the asymptotic squashing parameter, E, and the area of the bolt, A-. K is the self-intersection number of the bolt. Thus the spaces do not have spin structure if k is odd. At infinity, the squashed three sphere has k points identified around the U1 fiber. This means that the reference background, is Taub nut anti de Sitter, with k points identified. If k is greater than one, the reference background will have an orbifold singularity at the nut. However, as I said earlier, I shall take it that such singularities are harmless.
Action To calculate the action, one matches the Taub bolt solution on a squashed three sphere, to a Taub nut solution. To do this, one has to re-scale the squashing parameter, E, as a function of radius. The surface term in the action, is the same asymptotically for Taub nut and Taub bolt. Thus the action comes entirely from the difference in volumes. Action for k = 1 For k greater than one, the action is always negative, while for k=1, it is positive for small areas of the bolt, and negative for large areas. This behavior is similar to that for Schwarzschild anti de Sitter space, and might indicate a phase transition in the corresponding conformal field theory. However, as I will argue later, there are problems with the ADS, CFT duality, if k=1. On the other hand, our results seem to indicate that there will be no phase transition, if more than one point is identified around the fiber. It will be interesting to see if this is indeed the case, for a conformal field theory on an identified squashed three-sphere. In these Taub bolt anti de Sitter metrics, one can calculate the area of the Misner string, and the Hamiltonian surface term. Both will be infinite, but if one matches to Taub nut anti de Sitter on a large squashed three-sphere, the differences will tend to finite limits. As in the asymptotically locally flat case, the entropy is less than a quarter the area of the bolt, because of the effect of the Misner string. Entropy One can also calculate the entropy from the partition function, by the usual thermodynamic relations. The mass will be given by taking the derivative of the action with respect to beta. This is equal to the Hamiltonian surface term at infinity. The mass or energy, is the only charge that is constrained in the ensemble. The nut charge is fixed by the boundary conditions, and so doesn't need a La-grange multiplier. Thus the entropy is beta M, minus I. This agrees with the entropy calculated from the bolts and Misner strings, showing our definition, is consistent.Formally at least, one can regard Euclidean conformal field theory on the squashed three sphere, as a twisted 2+1 theory, at a temperature, beta to the minus one. Thus one would expect the entropy to be proportional to beta to the minus two, at least for small beta. This has been confirmed by calculations by Dowker, of the determinants of scalar and fermion operators on the squashed three sphere, for k=1. Dowker has not so far calculated the higher k cases, but one would expect that these would have similar leading terms, but with beta replaced by beta over k. The next leading order terms in the determinant, are beta to the minus one, log beta. No terms like this appear in the bulk theory, so if there really is an ADS, CFT duality in this situation, the log beta terms have to cancel between the different spins.
In fact, the scalar and fermion log beta terms will cancel each other, if there are twice as many scalars as fermions. This would be implied by super symmetry, suggesting that super symmetry is indeed necessary for the ADS, CFT duality.The Misner string contributions to the entropy are of order beta squared. Thus Dowker's calculations will have to be extended to this order, to k greater than one, to fermion fields with anti periodic boundary conditions, and to spin one fields. All this is quite possible, but it will probably require Dowker to do it. One might ask, how can a conformal field theory on the Euclidean squashed three sphere, correspond to a theory in a spacetime of Lorentzian signature. The answer is that, unlike the Schwarzschild anti de Sitter case, one has to continue the period, beta, to imaginary values. This makes the spacetime periodic in real time, rather than imaginary time. One gets a 2+1 rotating spacetime, rather like the Goedel universe, with closed time like curves. Although field theory in such a spacetime, may seem pathological, it can be obtained by analytical continuation, and is well defined despite the lack of causality. It is interesting that the analytically continued entropy, is negative, suggesting that causality violating spacetimes, are quantum suppressed. However, it is probably a mistake, to attach physical significance, to the Lorentzian conformal field theory. To sum up, I discussed the ADS, CFT duality in two new contexts. That of rotating black holes and that of solutions with nut charge. I showed how gravitational entropy can be defined in general. The partition function for a thermodynamic ensemble can be defined by a path integral over periodic metrics. The lowest order contributions to the partition function will come from metrics with a U1 isometry, and given behavior at infinity. The entropy of such metrics will receive contributions from horizons or bolts, and from Misner strings, which are the Dirac strings of the U1 isometry, under Kaluza Klein reduction. One would like to relate this gravitational entropy, to the entropy of a conformal field theory on the boundary. For this reason, we considered a new class of asymptotically locally anti de Sitter spaces. Other people have investigated the Maldacena conjecture, by deforming the compact part of the metric, but this is the first time deformed anti de Sitter boundary conditions, have been considered. We studied Taub bolt anti de Sitter solutions, with Taub nut anti de Sitter, as the reference background. The entropy we obtained obeyed the right thermodynamic relations, and had the right temperature dependence, to be the entropy of a conformal field theory, on the squashed three sphere. Because the Taub bolt solutions for odd k, do not have spin structures, this may indicate that the anti de Sitter, conformal field theory correspondence, does not depend on super symmetry.
I will end by saying that gravitational entropy, is alive and well, 34 years on. But there's more to entropy, than just horizon area. We need to look at the nuts and bolts.

What happens to a black hole after it forms? Does it vibrate? Radiate? Lose mass? Grow? Shrink?

Partial solutions of the Einstein equations point to two possible outcomes:

  • A non-rotating, spherically symmetric black hole, first postulated by Schwarzschild.
  • A rotating, spherical black hole, predicted in 1964 by the New Zealand mathematician Roy Kerr.

These two types of black holes have become known as Schwarzschild and Kerr black holes, respectively. Both types of black holes are "stationary" in that they do not change in time, unless they are disturbed in some way. As such, they are among the simple st objects known in General Relativity. They can be completely described in terms of just 2 numbers: their mass M and their angular momentum J.

Theoretically, black holes may also possess electric charge, Q, but it would quickly attract enough charge of the opposite sign. The net result is that any "realistic" or astrophysical black hole would tend to exhibit zero charge. This simplicity of black holes is summed up in the saying "black holes have no hair," meaning that, apart from its mass and momentum, there is no other characteristic (or "hair") that a black hole can exhibit.

(But things may not be quite so simple. Yes -- you've guessed it -- there's more to this story. To explore it, though, is beyond the scope of this exhibit.)

However, both the Schwarzschild and Kerr black holes represent end states. Their formation may result from various processes, all of them quite complicated. When a "real" black hole forms from, say, the collapse of a very mass ive star, or when a black hole is disturbed by, say, another black hole spiralling into it, the resulting dynamics cause disturbances in spacetime that should lead to the generation of gravitational waves.

By numerically solving the Einstein equations on powerful computers, scientists have been able to simulate the gravitational waves emitted by perturbed or interacting black holes. When visualized in movies generated by advan ced computer graphics, the unfolding wave patterns are not only intriguing but strikingly beautiful.

By emitting gravitational waves, non-stationary black holes lose energy, eventually become stationary and cease to radiate in this manner. In other words, they "decay" into stationary black holes, namely holes that are perfectly spherical or whose rotatio n is perfectly uniform. According to Einstein's Theory of General Relativity, such objects cannot emit gravitational waves.

 Eventually, it seems the black hole will get down to zero mass, and will disappear altogether. What then will happen to all the objects that fell into the hole, and all the people that either jumped in, or were pushed? They can't come out again, because there isn't enough mass or energy left in the black hole, to send them out again. They may pass into another universe, but that is not something that will make any difference, to those of us prudent enough not to jump into a black hole.

What are Gravitational Waves?

Predicted in Einstein's General Theory of Relativity, gravitational waves are disturbances in the curvature of spacetime caused by the motions of matter. Propagating at (or near) the speed of light, gravitational waves do not travel "through" spacetime as such -- the fabric of spacetime itself is oscillating. Though gravitational waves pass straight t hrough matter, their strength weakens proportionally to the distance traveled from the source. A gravitational wave arriving on Earth will alternately stretch and shrink distances, though on an incredibly small scale -- by a factor of for very strong sources. That's roughly equivalent to measuring a change the size of an atom in the distance from the Sun to Earth!

No wonder these waves are so hard to detect.

Are Gravitational Waves Real?

The first test of Einstein's General Theory of Relativity (the bending of light by the gravity of a large mass, seen in a solar eclipse) was made by a team led by Sir Arthur Eddington, who became one of the strongest supporters of the new theory. But when it came to gravity wave s, Eddington was skeptical and reportedly commented, "Gravitational waves propagate at the speed of thought."

Ed Seidel, NCSA/Univ. of Illinois, on-camera
Movie/Sound Byte
QuickTime Movie (1.0 MB); Sound File (615K); Text

Eddington was not the only skeptic. Many physicists thought the waves predicted by the theory were simply a mathematical artifact. Yet others continued to further develop and test the concept. By the 1960s, theorists had showed that if an object emits gravitational waves, its mass should decrease. Then, in the mid 1970s, American researchers observed a binary pulsar system (named PSR1913+16) that was thought to consist of two neutron stars orbiting each other closely and rapidly. Radio pulses from one of the stars showed that its orbital period decreases by 75 microseconds per year. In other words, the stars are spiralling in towards each other -- and by just the amount predicted if the system were losing energy by radiating gravity waves.

Why Should We Care About Gravity Waves?

Gravitational wave astronomy could expand our knowledge of the cosmos dramatically. For starters, gravitational waves, though weakening with distance, are thought to be unchanged by any material they pass through and, therefore, should carry signals unalt ered across the vast reaches of space. By comparison, electromagnetic radiation tends to be modified by intervening matter.

Aside from demonstrating the existence of black holes and revealing a wealth of data on supernovae and neutron stars, gravitational wave observations could also provide an independent means of estimating cosmological distances and help further our understanding of how the universe came to be the way it looks today and of its ultimate fate. Gravitational waves might unveil phenomena never considered before. Nature is smarter than any theorist trying to imagine or calculate what might be out there!

Sifting Through the Waves

From supercomputer simulations performed at NCSA and other advanced computational facilities, relativity researchers expect different types of cosmic events to possess characteristic gravitational wave signatures.

Consider the waves emitted by a single, distorted black hole, for example.

Distorted Black Hole

The remarkable thing about a black hole when simulated on a computer is that no matter how it forms or is perturbed, whether by infalling matter, by gravitional waves, or via a collision with another object (including a second black hole), it will "ring" with a unique frequency known as its natural mode of vibration. It's this unique wave signature that will allow scientists to know if they've really detected a black hole. But that's not all. The signal will tell them how big the black hole is and how fast it's spinning.

as I have written before and I would be thrilled if you post it is in the holgraphic principle there remains a higher dimension that explains why we can calculate facts about black holes. My theory suggests that this greater dimension may be interferring causing short grbs, also I have suggested possible brane GRBs appear to be divided into two classes: those shorter than 2 seconds, and those longer than 2 seconds. If this classification scheme is correct, then it would follow that there are two different causes for the bursts. However, there are other properties of the bursts which differ and could lead to alternative explanations. The jury is still out as to the classification scheme and the associated mechanisms, especially for the shorter class of bursts
SGR 1806-20 Blast
I noticed that seconds after the initial blast of light, a doppler-like wave emanated from that point and seemed to fly past the SWIFT camera. This "wave" appeared to be traveling at close to light speed, what was it's composition?
Referring Page:

Answer provided by Lynn Cominsky (SSU E/PO Director):
The wave in question represented the light coming from the SGR in the initial blast. The animation showed it as coming out afterwards, this was incorrect.

A common event often mistaken by people in the sky to be a Gamma-Ray burst is an Iridium Flare. If you visit this link, then put in your latitude and longitude, you will be able to see if there were any of these flares reported during this time.

Fomalhaut, a 200-million-year-old star, is a mere infant compared to our own 4.5-billion-year-old Sun. It resides 25 light-years away from the Sun. Located in the constellation Piscis Austrinus (the Southern Fish), the Fomalhaut ring is ten times as old as debris disks seen previously around the stars AU Microscopii and Beta Pictoris, where planets may still be forming. If our solar system is any example, planets should have formed around Fomalhaut within tens of millions of years after the birth of the star. The Hubble images also provide a glimpse of the outer planetary region surrounding a star other than our Sun. Many of the more than 100 planets detected beyond our solar system are orbiting close to their stars. Most of the current planet-detecting techniques favor finding planets that are close to their stars. "The size of Fomalhaut's dust ring suggests that not all planetary systems form and evolve in the same way — planetary architectures can be quite different from star to star," Kalas explained. "While Fomalhaut's ring is analogous to the Kuiper Belt, its diameter is four times greater than that of the Kuiper Belt."The astronomers used the Advanced Camera for Surveys' (ACS) coronagraph aboard Hubble to block out the light from the bright star so they could see details in the faint ring.

Doomed Star Eta Carinae

A huge, billowing pair of gas and dust clouds is the super-massive star Eta Carinae.

Even though Eta Carinae is more than 8,000 light-years away, features 10 billion miles across (about the diameter of our solar system) can be distinguished. Eta Carinae suffered giant outburst about 150 years ago, when it became one of the brightest stars in the southern sky. Though the star released as much visible light as a supernova explosion, it survived the outburst. Somehow, the explosion produced two lobes and a large, thin equatorial disk, all moving outward at about 1.5 million miles per hour. Estimated to be 100 times heftier than our Sun, Eta Carinae may be one of the most massive stars in our galaxy.

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Eyeguy wants to be friends

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A Martian Dust Devil Passes
we are so fortunate that the general science community is so benevolent with their freedom to access all sorts of wonderful information. This  awesome NASA pic is no exception. Moving pictures from the surface of Mars...?

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Our Business Philosophy

Our mission statement..... A Hitchhiker's Guide to the Moon

An Apollo astronaut on the moon with a lunar rover Imagine trekking in a lunar rover across miles of the Moon's rough surface. Your mission: to explore a crater with suspected deposits of ice.

Image left: When traveling on the Moon, don't forget your map!
Ion Thrusters Propel NASA into Future

We are a curious species with amazing capacities to imagine and dream. We wonder about what we cannot see, are fascinated by what we do not know and are driven to explore.
In keeping with our continuous quest for knowledge, President George W. Bush announced a new plan for NASA in Jan. 2004. A renewed focus on space exploration, he explained, would strengthen our leadership in the world, improve our economy and enhance the quality of our lives.

artist's conception of a Prometheus spacecraft The Vision for Space Exploration calls for human and robotic missions to the Moon, Mars and beyond. To realize these ambitious goals, we will need more powerful and efficient propulsion and power-generation systems -- systems that can thrust a spacecraft out of Earth's orbit to the far reaches of the Universe.