How would a hypothetical graviton escape a black hole?

[DaveC426913]

TL;DR

If gravity can be (eventually) explained by a force-carrying particle, surely it must be emitted from where the mass is - which is within in the BH's EH.

How can gravitons escape a black hole? Presumably they must, in order to have an external gravitational effect.

I'm sure this is a naive GR-based model of a BH. I guess a BH is a different animal in the QM world?

 

[PeterDonis]

How can gravitons escape a black hole? Presumably they must, in order to have an external gravitational effect.

No, they don't have to. The gravitational effects observed at any event in a spacetime are entirely due to what is present in the past light cone of that event. For any event outside the horizon, no event on or inside the horizon is in the past light cone, so no such event is relevant for determining the gravitational effects observed.

I'm sure this is a naive GR-based model of a BH.

No, a GR-based model has the property I just described. When you think in terms of "gravitons having to get out of the BH", you're thinking in terms of a naive QFT-based model of a BH--but even such a model will still have the property I described above, so there is actually no need to consider how gravity "gets out" of the BH in that model either. See below.

I guess a BH is a different animal in the QM world?

We actually don't know what kind of animal a BH is in the QM world, since we do not have a good theory of quantum gravity.

However, we do know that there is a well-defined quantum field theory of a massless spin-2 field, whose classical limit is General Relativity. This theory works similarly to quantum electrodynamics, which is the QFT of a massless spin-1 field. In both theories, you can, at least in perturbation theory, model the interaction (gravity or electromagnetism) as the exchange of virtual gauge bosons (gravitons or photons), and virtual particles have nonzero amplitudes to be exchanged between spacelike separated events, so they are not confined to light cones, and therefore virtual gravitons could, in principle, get out of a BH to mediate a gravitational interaction between the hole and something outside.

Note, however, that this viewpoint is heuristic and limited, for three reasons: (1) because it is based on perturbation theory, and it is not at all clear that perturbation theory is sufficient to model a BH; (2) because the QFT of the massless spin-2 field that I just described is not believed to be a viable fundamental theory of quantum gravity anyway, for various reasons that the margin of this post is too small to contain; and (3) because, as I said above, QFT still has the property I described at the start of this post, which means we don't actually need to invoke stuff like virtual gravitons escaping from a BH to explain the gravitational effects observed outside one.

See this article by John Baez for a similar answer to the above:

https://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/black_gravity.html

 

[DaveC426913]

No, they don't have to. The gravitational effects observed at any event in a spacetime are entirely due to what is present in the past light cone of that event. For any event outside the horizon, no event on or inside the horizon is in the past light cone, so no such event is relevant for determining the gravitational effects observed.

I kind of expected that the answer was "they don't have to", although I don't really understand the details.

If not from the mass, where do the particles themselves get emitted from?

 

[martinbn]

I kind of expected that the answer was "they don't have to", although I don't really understand the details.

If not from the mass, where do the particles themselves get emitted from?

What do you mean by the mass? The mass in not localized, it is not in the hole.

 

[PeterDonis]

If not from the mass, where do the particles themselves get emitted from?

The gravitational effects at any event are due to what is in the past light cone of that event. That will always include stress-energy (which is more than just mass) as the source of gravity. At least, it will in any realistic model.

 

[Demystifier]

The question by OP, that has been asked many many times by many others, contains several wrong assumptions.
1. It assumes that the gravitons responsible for the force are real. But in fact they are virtual gravitons appearing in Feynman diagrams, and virtual gravitons can be faster than $c$ and can escape from the black hole.
2. It assumes that the source of gravity is the matter. But in GR, the source of gravity is also the gravity itself.
3. It assumes that, if gravity is quantum, then it's made of moving gravitons, so gravity must be moving. But in fact gravitons are just the quantum variant of the gravitational waves, which are just one of many possible states of gravitational field. In addition to these moving states, there are also static states, static solutions of the gravitational field equations. The black hole is really described by such a static state of fields.

 

[DaveC426913]

In GR, the source of gravity is only the matter, but also the gravity itself.

Did you want to take another stab at that?

 

[Demystifier]

Did you want to take another stab at that?

I've edited and revised my explanation above.

 

[PeterDonis]

in GR, the source of gravity is also the gravity itself.

It is and it isn't. The source of gravity in GR is the stress-energy tensor. There is no stress-energy tensor associated with gravity itself. But the Einstein Field Equation is nonlinear, so it is possible to have curved spacetime solutions that are vacuum (zero stress-energy tensor) everywhere, which can be thought of as gravity sort of acting as its own "source".

See this Insights article and its follow-ups for more:

https://www.physicsforums.com/threads/does-gravity-gravitate-comments.833528/

 

[DaveC426913]

If true, this seems to answer the question in a way I can grok:

"Static gravitational fields do not require the exchange of gravitons; only changes in the gravitational field would be mediated by gravitons."
https://www.physicsforums.com/threads/how-can-gravitons-escape-a-black-hole.827873/post-5200157

True?

 

[Demystifier]

If true, this seems to answer the question in a way I can grok:

"Static gravitational fields do not require the exchange of gravitons; only changes in the gravitational field would be mediated by gravitons."
https://www.physicsforums.com/threads/how-can-gravitons-escape-a-black-hole.827873/post-5200157

True?

Sort of true, yes, even if not perfectly precise.