Stephen William Hawking‘s final black hole research paper before his death on Einstein’s birthday, Black Hole Entropy & Soft Hair, has been released via Cornell University Library. The paper was written in collaboration with Cambridge and Harvard researchers, Sasha Haco, Malcolm J. Perry and Andrew Strominger.
The paper deals primarily with the conundrum know as the Information Paradox which states that information (underlying quantum wave-function) can never be destroyed and that information taken into a black hole can never escape, yet, black holes, as Hawking posited in the 1970s, have a temperature and since they have a temperature they will eventually dissipate and if they dissipate then so too shall the information there contained, thus engendering a paradox. Something that theoretically cannot happen MUST happen as per the theory. If the information cannot be destroyed but cannot escape, then where does it go? Does it go anywhere?
Two prominent lines of argument arose:
- Black don’t actually evaporate. Hawking was wrong.
- Or, black holes DO evaporate. Hawking was right. The information is hyper-compressed into a space which remains after a black hole vanishes.
Hawking, Strominger, Perry and Haco instead posit that a black hole’s outgoing radiation (Hawking Radiation) is imprinted with the information previously imprinted on the black hole on photons which Strominger termed “soft hairs” and is thus returned to the universe, resolving the paradox. Neither soft hairs nor Hawking Radiation has been proven to exist but it makes sense via the formal logic being applied to black holes. Hopefully, it can, at the least, be utilized as a stepping stone for physicists studying black holes moving forward.
The abstract to the monograph is provided below.
Abstract: A set of infinitesimal Virasoro L ⊗ Virasoro R diffeomorphisms are presented which act non-trivially on the horizon of a generic Kerr black hole with spin J. The covariant phase space formalism provides a formula for the Virasoro charges as surface integrals on the horizon. Integrability and associativity of the charge algebra are shown to require the inclusion of ‘Wald-Zoupas’ counterterms. A counterterm satisfying the known consistency requirement is constructed and yields central charges cL = cR = 12J. Assuming the existence of a quantum Hilbert space on which these charges generate the symmetries, as well as the applicability of the Cardy formula, the central charges reproduce the macroscopic area-entropy law for generic Kerr black holes.
PDF of the paper: Hawking et al. (2018) Black Hole Entropy & Soft Hair