Quantum black hole entropy and Newton constant renormalization.

Abstract

We discuss the status of the black hole entropy formula ${\mathit{S}}_{\mathrm{BH}}$=${\mathit{A}}_{\mathit{H}}$/4G in low-energy effective field theory. The low-energy expansion of the black hole entropy is studied in a nonequilibrium situation: the semiclassical decay of hot flat space by black hole nucleation. In this context the entropy can be defined as an enhancement factor in the semiclassical decay rate, which is dominated by a sphaleronlike saddle point. We find that all perturbative divergences appearing in Euclidean calculations of the entropy can be renormalized in low-energy couplings. We also discuss some formal aspects of the relation between the Euclidean and Hamiltonian approaches to the one-loop corrections to black hole entropy and geometric entropy, and we emphasize the virtures of the use of covariant regularization prescriptions. In fact, the definition of black hole entropy in terms of decay rates requires the use of covariant measures and, accordingly, covariant regularizations in path integrals. Finally, we speculate on the possibility that low-energy effective field theory could be sufficient to understand the microscopic degrees of freedom underlying black hole entropy. We propose a qualitative physical picture in which black hole entropy refers to a space of quasicoherent states of infalling matter, together with its gravitational field. We stress that this scenario might provide a low-energy explanation of both the black hole entropy and the information puzzle.