I’ve been going through M.I.T.’s 8.821, and am thoroughly, undeniably, hopelessly stuck – as I have been for approximately two months – on the eighth question of the sixth problem set, which can be found here. You could, in fact, say that there’s a mass[ive] gap in my understanding.
That painfully bad joke made, the problem reads:
“The event horizon is a global notion that depends strongly on the asymptotics of the space in which the black hole sits. Prove a version of the Area Theorem for asymptotically AdS spaces. The definition of event horizon for asymptotically AdS spaces, I believe, is (brace yourself): the boundary of (the past of (the intersection of (future timelike infinity) with (the conformal boundary of AdS))).”
I feel (and another friend agrees) that there must be a substantial difference between the asymptotically locally AdS case and the asymptotically AdS scenario. I can deal with the former, but the question remains:
How does one generalize from the asymptotically locally AdS case to the asymptotically AdS case?
I read this immediately prior to going through the set, but the solutions described inside require the black hole boundary n−1 to be sufficiently smooth; I’m looking for something that addresses not-quite-so-regular horizons.