# Are horizons fingerprints of General Relativity ? and more questions

• lalbatros
In summary: There are many indications for the existence of horizons, both from experiments and from mathematical models of gravitational field theories. Some of the most compelling evidence comes from the study of black holes. A black hole is a region of space in which the gravitational force is so strong that nothing, not even light, can escape from it. As you might know, when an object approaches a black hole, its gravity causes it to start sucking in matter and energy from around it. Eventually, the object becomes so densely packed with mass that the laws of physics no longer apply to it. In this extreme situation, it is as if the object has disappeared from the rest of the universe.
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

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.

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

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.

Michel

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

Are horizons predicted by gravitation theories generally?

Hi again, Michel,

lalbatros said:
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.

lalbatros said:
[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.

lalbatros said:
[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

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## 1. What is General Relativity?

General Relativity is a theory of gravity developed by Albert Einstein in the early 20th century. It describes how massive objects interact with each other and how space and time are affected by gravity.

## 2. How do horizons relate to General Relativity?

Horizons, such as the event horizon of a black hole, are a consequence of General Relativity. They are regions of space where the gravitational pull is so strong that not even light can escape.

## 3. Are horizons unique to General Relativity?

No, horizons can also be found in other theories of gravity, such as Newton's theory of gravity. However, General Relativity offers a more accurate and complete description of horizons.

## 4. How do horizons act as fingerprints of General Relativity?

Horizons have specific properties, such as their size and shape, that can only be explained by the principles of General Relativity. This makes them a unique and important feature of the theory.

## 5. Is there any evidence for the existence of horizons predicted by General Relativity?

Yes, there is strong evidence for the existence of horizons from various astronomical observations, such as the behavior of stars and light near black holes. This evidence supports the validity of General Relativity.

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