Before getting to his comments, let me say a few things about what I did in the paper.
A. The "white hole" I analyzed is just a classical background which is the time reversal of (part of) a black hole spacetime. The initial data for this spacetime can be obtained from a spacelike slice across the usual black hole spacetime ("after" the horizon has formed), and need not include the singularity.
B. I imposed the condition of isolation (vacuum) outside the white hole at early times. This is equivalent to requiring no radiation in the future of the original black hole spacetime. An unusual boundary condition, but corresponds to the "isolated" white hole I was interested in investigating.
C. I used Hawking's method (i.e., Bogoliubov transformation of in- and out- modes) to study the future behavior of the white hole, or, equivalently, the initial preparation of the black hole required to prevent it from radiating.
It should be clear from the summary that my paper can be read as merely analyzing the black hole spacetime with a nonstandard future boundary condition and then interpreting the results in time reversed language. ("Look ma, no white hole"!) That is, the methods I use have exact time reversal invariance built in. In the paper I note that an isolated white hole and an isolated black hole behave differently. That is not a violation of time reversal invariance applied to an entire spacelike slice because the time reversal of an isolated black hole (which radiates into its future) is not an isolated white hole -- rather, it is a white hole bathed in incoming radiation (from its past) at the Hawking temperature (see figures in the paper). However it does contradict the idea that the time reversed evolution of the hole can be understood independently of its environment (i.e., what is outside its horizon).
Lubos makes a number of remarks in his blog post. I try to summarize them below, together with my comments. He may make other claims as well that I haven't addressed.
1. We know from string theory that black holes and white holes are the same thing. Well, let me first point out that not everyone believes in string theory as the correct theory of quantum gravity (i.e., describing our universe) at 99.9 percent confidence level. Secondly, if a semi-classical calculation like mine suggests differences between the behavior of an isolated white hole and an isolated black hole, isn't it interesting to reconcile that with what AdS/CFT predicts? Although I am not an expert on AdS/CFT I suspect that the time reversal invariance of the CFT boundary state only implies time reversal of the entire bulk state (i.e., on an entire spacelike slice) and not of the black hole alone. If so, there is no contradiction with my results -- see above. Perhaps someone can clarify this for me?
2. Hawking clearly said the same in his 1976 paper. That was my impression on first reading, but since all of his arguments center on the case of a black hole in equilibrium with a bath at equal temperature, it is unclear (at least to me) how this can be generalized to an isolated white hole. That was one motivation for my investigation.
3. Entropic arguments imply that white holes (as obtained via (A) above) are extremely unlikely: specifically, a highly entropic white hole should not explode into lower entropy ejecta. I understand the argument but don't place as much confidence in it as Lubos does. The uncertainty is not about the 2nd Law but about the interpretation of black or white hole entropy.
Lubos does not want me to consider classical spacetimes generated by the initial data obtained in (A) above. Even if one accepts that such spacetimes are highly improbable, that does not mean that they shouldn't be studied. (For example, if you are a many worlder there are some branches on which exploding white holes are observed!) Apparently it is in bad taste to think about (exploding) white holes, but perhaps Lubos should tell this to, e.g., Frolov and Novikov.
Now, a little analysis of the cognitive dissonance (conflicting priors ;-) between Lubos and me. When I say "white hole" I mean the time reversal of some classical black hole spacetime. I consider this (time reversed) spacetime of theoretical interest, even if it results from strange initial conditions. I use what I know (general relativity + quantum fields in slightly curved space) to probe the more mysterious issues (black hole entropy, quantum gravity, ... ). This follows Wheeler's approach of "radical conservatism" -- take the physics you trust with high confidence, and extrapolate to extreme conditions until something interesting happens! Lubos is a true believer in string theory, so to him a black hole is this stringy thing about which we already know almost everything, including that its entropy is due to countable internal microstates, it is dual to some YM configuration through holography, etc. This will likely elicit a shriek of anger from Lubos (or he will just call me dumb), but I consider all of those claims plausible but perhaps not true in our universe: string theory may turn out not to describe Nature.
Finally, there is also some discussion of my paper here and here, but it seems that both authors are slightly confused about the results (perhaps this is my fault for not being clear :-). For example, the requirement that white holes "explode" is not a consequence of my analysis, but just follows from time reversal of the black hole formation event (see, e.g., Frolov and Novikov or figures in the paper). I am only studying the quantum effects (i.e., equivalent of Hawking radiation), which are a correction to the classical evolution.
Further discussion in a follow up post about white/black hole entropy.