Can a trapped surface be formed without any massive bodies inside that trapped surface, but only by a configuration of massive bodies surrounding the trapped volume?

  • $\begingroup$ It seems obvious that the answer is no, if you interpret photons and gravitons as massive bodies, but it is not immediately obvious how to prove it, because of the problem of localization of stress energy in GR. $\endgroup$ – Ron Maimon Aug 31 '11 at 21:52

If I understand your question correctly, the answer is yes, by virtue of the fact that trapped surfaces can form without there being any massive bodies in the universe whatsoever. In other words, trapped surfaces can form purely from the focusing of gravitational waves. Now take some massive bodies all very far apart from each other, and shake them vigorously. If the shaking is hard enough, the profile of the gravitational waves would be sharp enough that the results in the linked paper would (in principle) apply.

  • $\begingroup$ I think the proper interpretation of the question is to include gravitational waves as bodies, at least, this makes it more interesting. But your answer is 100% correct, of course, +1. $\endgroup$ – Ron Maimon Aug 31 '11 at 21:51

By definition future directed geodesics emanating orthogonally from a trapped surface either outwards or inwards have to converge in finite time. Important thing to note is that this affine distance in which this convergence has to happen goes inversely with the curvature of the trapped surface and doesn't depend on any finer detail of the situation.

If mass is existing outside such a surface then one has to ask the question of what is keeping it stable there? Why are they not falling in?

I can't see how I can rule out such a case if say the mass is placed such that it is outside this converging distance (which is intrinsically determined by the trapped surface only).

Not sure how good an example this is..but one can always have stable orbits of small amounts of matter around a Schwarzschild black hole and every spherical surface inside the event horizon is a trapped surface in this case. So in some sense there is no matter inside any of the trapped surfaces. (but this orbiting small object is a matter outside all the trapped surfaces)


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