Stephen Hawking's final paper that he and his colleagues completed just days before his death has now been published. It's titled "Black Hole Entropy and Soft Hair," co-authored with Sasha Haco, Malcolm J. Perry, and Andrew Strominger, about the black hole information paradox. Here is the abstract:
A set of infinitesimal VirasoroL⊗VirasoroR 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.
The Guardian has a translation:
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In the latest paper, Hawking and his colleagues show how some information (contained in an object that falls into a black hole) at least may be preserved. Toss an object into a black hole and the black hole’s temperature ought to change. So too will a property called entropy, a measure of an object’s internal disorder, which rises the hotter it gets.
The physicists, including Sasha Haco at Cambridge and Andrew Strominger at Harvard, show that a black hole’s entropy may be recorded by photons that surround the black hole’s event horizon, the point at which light cannot escape the intense gravitational pull.