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Is it possible for there to be an object so massive and/or dense that it absorbs its own gravitational energy? I ask this because it occurred to me that if gravity is a type of energy than by the mass energy equivalence the gravitational energy should also have mass, which should be affected by the gravity. Is it possible for this gravitational energy to be sucked back into the object that created it?

tox123
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For this to happen, you have to consider two things:

  1. the background geometry set up by the object, initially.
  2. subsequent gravitational radiation

Einstein's equation is nonlinear, which means that it is possible for gravitational radiation, unlike classical electromagnetic radiation, to interact with the background static field. In particular, this paper:

https://arxiv.org/pdf/gr-qc/0105042.pdf

Claims that it is actually possible to create backscattering of gravitational radiation generated near a Schwarzschild black hole back into the black hole. I haven't read it beyond the abstract, but the conclusion seems reasonable, and the mehtodology, from skimming, seems reasonable as well.

Zo the Relativist
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  • And yes, quibblers, if this works for perturbations of a schwarzschild spacetime, it will also work for a sufficiently small collapsing matter distribution, because the two are externally indistinguishable by Birchoff's theorem. – Zo the Relativist Aug 04 '17 at 20:36
  • We are not quibblers, (some of us anyway), but a small nitpicky point. I don't think there are any real Schwarzschild solutions, but your answer still applies to anything with angular momentum? I need to check this myself, so I am not asking you, but I must check if Birchoffs theorem applies to blackholes with less simple event horizons. Or is this precisely your point about what a perturbation implies? –  Aug 04 '17 at 21:42
  • @Countto10: Birchoff's theorem only applies in spherical symmetry. while the exact schwarzschild solution is a fine-tuning of angular momentum, kerr solutions can get arbitrarily close to schwarzschild in the exterior region, which is all that matters here. The exterior of a collapsing dust shell with low angular momentum would be a very close approximation of the schwarzschild solution, whihc is why you are able to use Schwarzschild for things like the bending of light by the sun. – Zo the Relativist Aug 04 '17 at 22:04
  • Thank you very much for the answer, as a self study person, it saves me hours of research, in many cases. Regards –  Aug 04 '17 at 22:33
  • The paper mentioned by @Jerry Schirmer is not that all the gravitational radiation is reabsorbed by the BH. Not all of it, it just represents back scattering. The max says the paper is about 50%. I took the question to mean that it absorbs it all. The only way is if any gravitational radiation happens inside the horizon it'll stay inside. BTW, it is also true that incoming gravitational radiation from outside the BH will also typically not all be absorbed, unless the incident angle is zero (and then I'm not sure). Some will be scattered. The cross sections have been calculated for some cases. – Bob Bee Aug 05 '17 at 00:23