Are horizons fingerprints of General Relativity ? and more questions

[lalbatros]

Are horizons fingerprints of General Relativity,
or should I reasonnably expect them in any theory of gravitation ?

If you believe that horizons should be expected in most theories,
what are the physical reasons, how could I conceive horizons as unavoidable ?

On the contrary, why and how would you justify that horizon should not occur ?

Are there experimental indications for the existence of horizons ?

What are the mathematical conditions for the occurence of an horizon ?

How and why was physics led to this new concept ?

Thanks to enlarge my horizon on this topic!

Michel

 

[pervect]

Horizons come up in the simple case of the coordinate system of an accelerating observer in special relativity - the so called Rindler horizon which I've talked about before. A link which talks about this only in SR terms (but is still somewhat advanced) is

http://gregegan.customer.netspace.net.au/SCIENCE/Rindler/RindlerHorizon.htm

A link to gravity is the equivalence principle, which suggests that the coordinate system of an accelerating spaceship is a useful analogy to a gravitational field.

 

[Demystifier]

In other words, horizons are fingerprints of special relativity in noninertial frames.

 

[lalbatros]

Demystifier,

In other words, horizons are fingerprints of special relativity in noninertial frames.

Could we not even say that the full SR is not needed ?

Is it not enough to assume that accelerated particles can never exceed the speed of light: v<=c ?
Indefinitively accelerated particles will reach c assymptotically. This assymptote divides the space in two half. One of these half-space can interact with the accelerated particle. The other half-space can never interact with it: an horizon appears (Rindler).

The EP makes the bridge to gravitational fields.

Thanks for your decisive help.

Michel

 

[Demystifier]

In GR you require that metric locally takes a Minkowski form. For that reason, I think that SR is needed.

 

[Chris Hillman]

Are horizons predicted by gravitation theories generally?

Hi again, Michel,

Are horizons fingerprints of General Relativity,
or should I reasonnably expect them in any theory of gravitation ?

If you believe that horizons should be expected in most theories,
what are the physical reasons, how could I conceive horizons as unavoidable ?

There are several things you might mean by "unavoidable" here. I will interpret your question as follows: if we construct a viable relativistic classical field theory of gravitation (any such theory must neccessarily closely mimic gtr), and study the spherically symmetric vacuum solutions to the field equations in our theory, should we expect to find that event horizons are predicted by this theory? (Clearly, this is a rather limited interpretation of when a theory can be said to "predict event horizons", but at least it is comparatively straightforward to check!)

Many people have tried to construct relativistic classical field theories of gravitation which are viable but which do not admit event horizons in this sense, or in some similar sense. As far as I know (after discounting erroneous claims), none have succeeded, and there quite a few reasons why one should expect this programme to be very difficult.

For example, in gtr, a supermassive black hole is predicted to have an event horizon located in a region of comparatively low curvature, so we might expect this qualitative feature to be hard to avoid in any theory which closely resembles gtr in spacetime regions having comparatively low curvature. You can probably think of objections to this reasoning--- certainly it is not a proof!--- but more elaborate arguments can be given.

I should add that there are many alternatives to gtr which have been suggested. Those which are well defined can generally be expressed by writing down some kind of action principle (as can gtr) in which the gravitational term(s) differ from gtr. Many of these theories have the property that, like gtr, their spherically symmetric vacuum solutions possesses event horizons, and some do not. The latter group (at least, the theories I know about) consists of theories which are known to be inconsistent with at least some well-established experimental or observational evidence.

It is possible to study large CLASSES of relativistic classical field theories of gravitation all at the same time, and to show that whole CLASSES have the properties that they predict horizons in the sense above while agreeing with available evidence. Similarly, one can show that large classes of theories which do not predict horizons in the sense above must all DISAGREE with some evidence. However, it is always possible that someone might come up with a radically new theory not belonging to either of these classes, and which "achieves the miracle" desired by some. I don't see much hope of decisively ruling out this possibility entirely.

[Are there experimental indications for the existence of horizons ?

Oh gosh, yes! Here is a page which is quite out of date but which might help you scan the arXiv (or press releases from universities where astronomers have been studying this question) for more up to date information: http://www.math.ucr.edu/home/baez/RelWWW/tests.html#bh .
Incidently, be careful in reading press releases--- they tend to be hyped rather shamelessly, like any other form of self-promotion.

[What are the mathematical conditions for the occurence of an horizon ?

Well, there are many types of horizon; you probably want either "event horizon" or the much easier concept of "Killing horizon". The definitions are rather technical; see for example Hawking and Ellis, The Large Scale Structure of Space-Time, Cambridge University Press, 1973. A crucially important point about the difficult notion of an event horizon is that this concept has a profoundly "teleological" nature. Some pictures illustrating this very clearly, using thought experiments involving the Vaidya null dust solution, can be found in Frolov and Novikov, Black Hole Physics, Kluwer, 1998.

Chris Hillman