## Black Hole Information Loss Question

 Quote by Chalnoth ... Anomaly cancellation arises when you consider moving bodies.... It turns out that the gravitational field itself depends not just upon where the object is, but also, in General Relativity, depends upon the object's velocity and even acceleration. For moving objects, these additional velocity and acceleration terms serve to exactly cancel with the fact that gravity propagates at a finite speed, so that the gravitational pull points directly at the moving object...
Chalnoth, does this imply greater than c propagation of gravity, or is space-time warped to accommodate it?

 Quote by Mark M I don't know if MTW is very good for a first textbook on GR (because of it's complexity). I think Sean Carroll's lecture notes are a bit easier for a beginner.
Mark, Can I confirm, are you referring to the lecture notes from '97?

Regards,

Noel.
 Yes, they're from 1997. They're a pretty fair introduction to the topic. The text that Chalnoth mentioned is arguably the best resource ever written regarding GR, but it's a monster.

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 Quote by Lino Chalnoth, does this imply greater than c propagation of gravity, or is space-time warped to accommodate it?
Not at all. A better way to understand it is that the curved space-time moves along with the moving object, though if the object changes its acceleration, the space-time won't be able to keep up and it will emit gravitational waves instead.

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 Quote by Lino does this imply greater than c propagation of gravity
No. My attempt at a non-technical explanation (I probably have introduced some inaccuracies:
 Quote by George Jones Newtonian gravity predicts closed circular and elliptical orbits. This prediction depends on the fact that Newtonian gravitational force is directed along the line joining the instantaneous positions of objects, like the Earth and the Sun. If Newtonian gravitational force weren't directed along this line, orbits wouldn't be closed. As the Earth orbits the Sun, the position of the Sun, relative to Earth, changes. If gravity propagates at the speed of light, shouldn't the Earth feel (gravitationally) where the Sun was (according to the Earth) eight minutes ago, that is, shouldn't gravitational force be directed along the line that joins where the Earth is now to where the Sun was eight minutes ago? And if this is true, then, according to the previous paragraph, how can the Earth's orbit be a closed ellipse? To answer these questions, I am going to talk briefly about the main equation of Einstein's theory of gravity, general relativity, G = T. Here, G is a geometrical quantity that depends on the curvature of spacetime, and T is a physical quantity that depends on the distribution and flows of mass and energy in the universve. In Einstein's theory, gravity is a manifestation of spacetime curvature. If T depends not only on position, but also on flow of matter, then (by the equals sign) G, spacetime curvature, and (thus) gravity are affected by the velocities of objects. This feature is not present in Newtonian gravity. As an example, consider a uniformly dense planet. According to Newton, the gravitational field of the planet is independent of the spin of the planet. According to Einstein, however, a planet's gravitational field is not independent of its spin. Spin puts the matter of the planet in motion, so different spins give different gravitational fields. To test this for the Earth, a satellite carrying gyroscopes has been put into orbit. Back to the Earth and Sun. Form the point of view of the Earth, the mass of the Sun moves, and so, according to Einstein, this motion contributes to the gravitational field of the Sun. The field of the Sun depends on where the Sun is, and on how the Sun moves. These two contribution's to the Sun's gravitational field, position and velocity, add to produce an "effective force" that *appears* to point towards where the Sun is now, not where it was eight minutes ago. What happens if the Sun magically disappears? The Earth will continue on in its orbit for another eight minute under the influence of an "apparent force" directed towards where the Sun would have been. After eight minutes, the Earth realizes that the Sun isn't there, and stops orbiting the missing Sun.
 Thanks all. Much appreciated. Regards, Noel.

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Leonard Susskind has a very interesting book for the general public.....non mathematical : THE BLACK HOLE WAR
[My battle with Stephen Hawking to make the world safe for quantum mechanics] 2008

[Lots of interesting insights often from a somewhat different perspective.]

This book is about Hawkings original claim that information is lost and Susskind's refusal to accept that premise. Hawking seems to have acknowledged Susskind was one of the first to realize the implications of 'black hole information loss. Susskind says he finally prevailed via the Holographic principle, ADS/CFT, although Hawking needed a different perspective to convince himself some years later that he was wrong. Susskind concludes the book with an Epilogue referring to 2002:

 Roger [Penrose] [still!!!!] maintained Stephen was right and he and Stephen continued to believe {that information was lost} .....I was surprised since ...as far as anyone who had been following recent developments was concerned, Matrix Theory, Maldacena's discovery, and Strominger and Vafa's entropy calculations had finally put the question to rest....In a press conference in 2004 Hawking [finally] announced he had changed his mind...I [recently] learned Don Page had a made a similar bet in 1980 [to Susskind's] ...on April 23, 2007, two days before I wrote this paragraph, Stephen formally conceded....[to Page] ....
There is a photocopy of Hawking's concession note to Page, signed via Hawkings thumprint!!

Susskind says further:
 ..Although the issue of whether information is lost in black holes....has now coalesced around a new paradigm,...I doubt we have learned all its important lessons. ..At the moment no one knows how to apply String Theory, the Holographic principle [and Maldacena's ADS/CFT correspondence in anti de Sitter space] to cosmic horizons....
Radiation, degress of freedom, and particle production associated with cosmic horizons has been the subject of several recent threads and ARXIV papers in these forums.

It turns out that entropy, [a subset of information theory] and particle production as well, can be associated with a variety of horizons, even the Hubble sphere which has not usually been thought of that way in these forums:

one such is here:

http://arxiv.org/abs/1207.0505

and the discussion:

 ...This bulk volume is taken to be the Hubble volume in which the enclosed bulk space is taken to be the cosmic space that has already emerged; The surface is the Hubble sphere. The emergence of matter [degrees of freedom] along with cosmic space occurs during the current expansion era when the universe is making the transition from one de Sitter phase to another.
and Ted Jacobson's foundational 1995 paper:

 ...That causal horizons {They don't have to be event horizons.} should be associated with entropy is suggested by the observation that they hide information. In fact, the overwhelming majority of the information that is hidden resides in correlations between vacuum fluctuations just inside and outside of the horizon.....
Thermodynamics of Spacetime:
The Einstein Equation of State
 Thanks Naty1. Another one for my reading list, but I think that I will bump this one up the list. Regards, Noel.
 Can someone explain to me what a tachyon is?

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 Quote by Alex1 Can someone explain to me what a tachyon is?
A tachyon is a hypothetical (and almost certainly impossible) particle that has negative mass squared. The negative mass squared causes the tachyon to have a speed which always exceeds that of light. As its kinetic energy approaches zero, its speed diverges to infinity. As its kinetic energy approaches infinity, its speed approaches the speed of light. These are probably impossible because if any existed and had any interactions at all with other matter, then they would basically cause the universe to explode.
 Haha Damn lmao that would suck good thing they don't. So basically the tachyon is really just a solution to an obsolete bosonic string theory?

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