Stephen Hawking's Black Hole 2004

Back from vacation and eager to see/hear informed comments on Hawking's Dublin presentation of his conclusion that black hole formation and evaporation does not involve a loss of information.

John Baez (math: U C Riverside) for provides a transcript of Hawking's talk, as well as comments about the technical details of Hawking's calculation. ( a link to Baez's discussion appears on the General Relativity 17 conference home page ).

John Preskill (physics: Cal Tech) comments on Hawking's talk and the link to a pdf file containing the text of a Preskill seminar at Cal Tech dealing the the black hole information paradox.

Sean Carroll (physics: U. of Chicago) discusses Hawking's talk on Chicago Public Radio (with Juan Maldacena of the Institute of Advanced Study at Princeton) where both give a discussion in lay terms of the significance of Hawking's talk and the problem in general. The talk appears on the Odyssey program for July 22, 2004.

Sean Carroll is one of the few first rank physics researchers who cares enough about public outreach (this of course is my characterization!!) to write a regular blog, which covers many interesting topics.

Hawking's results are derived (the details remain to be published) using an approach to quantum gravity in ordinary four dimensional spacetime (three spatial plus one time dimension) which uses the "Euclidean" version of the Feynman path integral (t -> it), with the approximate final answer analytically continued back to the "real world" via the inverse Wick rotation (it -> t ) . The exact answer requires integrating over all 4D geometries possible in the Euclidean space (which has four spatial dimensions). As Baez discusses (see above) , no one knows how to sum this Feynman path integral (FPI) formulation in four dimensions over all possible geometries.

Baez discusses how Hawking uses a "semi-classical" approximation which involves including only contributions from geometries "close to some solution of the classical equations of general relativity." Hawking includes the FPI contributions from only two such classical solutions.

Jacques Distler (U. Texas physics ) , a noted string theorist, notes that Hawking has to include an extra term, "a small negative cosmological constant", in the Lagrangian to keep the expression well defined at low energies. Distler notes that Hawking doesn't really deal with how that mathematical device allows a description finally in terms of the observed universe.

Distler also considers the black hole information paradox as "solved" in principle by string theorists for a multi-dimension version of the universe possessing "AdS/CFT" . In his Dublin talk , Hawking says:

"Finally, it was claimed that the issue was settled in favour of conservation of information, by ADS, CFT. ADS, CFT, is a conjectured duality between supergravity in anti de Sitter space, and a conformal field theory on the boundary of anti de Sitter space, at infinity. Since the conformal field theory is manifestly unitary, the argument is that supergravity must be information preserving. Any information that falls in a black hole in anti de Sitter space, must come out again. But it still wasn't clear, how information could get out of a black hole. It is this question, I will address. "

Hawking is trying to understand this problem in ordinary 4D spacetime.

An interesting approach to the black hole information paradox is contained in a recent preprint: "Black holes Conserve Information in Curved-Space Quantum Field Theory", by Christoph Adami and Greg L. Ver Steeg. The abstract is:

" We show that black hole formation and evaporation in curved-space quantum field theory is unitary if stimulated (as well as spontaneous) emission at the event horizon is taken into account. In particular, we show that the entropy accreted by a black hole when particles cross the event horizon is exactly balanced by a commensurate entropy increase of the rest of the universe, owing to the quantum entanglement between the black hole, Hawking radiation, and scattered radiation (including stimulated emission). As a consequence, the emitted radiation is non-thermal, and information can be retrieved using standard error corrections methods for noisy quantum channels."

The authors analyse the problem using quantum information theory instead of thermodynamics. In their conclusion, they state:

"In conclusion, we found that a consistent treatment of black hole dynamics requires the presence of emitted radiation outside the event horizon beyond the usual Hawking radiation. The radiation field in this region is non-thermal, while accretion and evaporation described by the Hamiltonian Htot = H + Hs is unitary. This guarantees that any change in the entropy of the inside region is exactly balanced by a commensurate change in the outside, so that the total entropy of the universe is constant under this dynamics. The information dynamics of black holes surprisingly turns out to be that of a
very standard quantum channel that is used to transmit classical information, where Hawking radiation provides the noise source. We further note that this solution to the black hole information paradox does not require to go beyond curved-space quantum field theory."