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:
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. They call this sheen of photons "soft hair".
"What this paper does is show that 'soft hair' can account for the entropy," said Perry. "It's telling you that soft hair really is doing the right stuff."
It is not the end of the information paradox though. "We don't know that Hawking entropy accounts for everything you could possibly throw at a black hole, so this is really a step along the way," said Perry. "We think it's a pretty good step, but there is a lot more work to be done."