Object so massive that it absorbs its own gravitational field?

Question

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?

Answer 1

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.