Date: Thu, 2 Apr 2015 15:43:26 -0400 From: Warren D Smith <warren.wds@gmail.com> To: math-fun <math-fun@mailman.xmission.com> Subject: [math-fun] Hawking black hole info paradox -- solved? Looks like it. http://arxiv.org/abs/1503.01487 Anshul Saini, Dejan Stojkovic: Radiation from a collapsing object is manifestly unitary Phys.Rev.Lett. 114,11 (2015) 111301

This claims to explicitly calculate the full density matrix, i.e. including all off-diagonal terms, of the Hawking radiation from a "collapsing shell" model of a black hole. It stays unitary at all times. Thus the Hawking "information loss paradox" actually does not occur.

It looks to me, at least on the surface, like they've really done it, and they didn't need to do anything crazy.

--Corrections. The "density matrix" in quantum mechanics is NOT unitary, it is (for a "pure state") of rank-1. (It is in this case of countably infinite order.) What I meant was, the density matrix M evolves via conjugation by a time-dependent unitary matrix U(t): M(t) = Uconjugatetranspose M U and they've apparently demonstrated that M remains of rank=1 and with |trace|=1, which is consistent with that.