This is a follow-up on a previous daylog.
In that daylog I mentioned that I was puzzling over the question of whether GR is time reversal invariant. Specifically, I was thinking of a star collapsing to form a black hole and releasing gravitational radiation. When time reversed, this process would seem to involve gravitational waves hitting the black hole and causing the event horizon to disappear and a star to form. This doesn't make a lot of sense and is not allowed in GR, so I was wondering a) Is GR time reversal invariant and b) If so, how do you think about the time reversal of a black hole collapsing?
And the answer is...over my head, apparently, but the short answer to a) is yes, and I'll explain about b). At the end of last week I spoke to a post doc who knows something about GR about this question. He said a lot of stuff I didn't understand, involving conformal transformations of spacetime and touching on the causal structure of anti-de Sitter space, but he did say a few things I understood. He said that yes, GR is time reversal invariant, but you have to determine correctly how all the relevant properties transform under time reversal. In the case of a black hole, when you think about it evolving in reverse it becomes a white hole. In this case, the reverse evolution is gravitational waves hitting a white hole and turning it into a star. That's still hardly intuitive, but at least it doesn't seem to clearly break any of the rules of GR. It is still unclear to me what time reversal really means in general in GR, but he said in cases like those considered in numerical GR, the geometry of all of spacetime is determined by the metric and its derivatives on one spacelike hypersurface (one surface of constant time in some coordinate system). In order to "time reverse" this solution in GR, one needs only to reverse the derivatives of the metric appropriately. So, that sort of answers the question. It defuses the core of my confusion, but, unfortunately, it seems I don't understand enough GR to really appreciate why this is the correct way to do time reversal.