Quantum black hole entropy and Newton constant renormalization

TL;DR

This paper examines the black hole entropy formula within low energy effective field theory, exploring its renormalization, the relation between Euclidean and Hamiltonian approaches, and proposing a low energy explanation for black hole microstates.

Contribution

It demonstrates that perturbative divergences in black hole entropy calculations can be renormalized using low energy couplings and discusses the potential of effective field theory to explain black hole microstates.

Findings

Perturbative divergences are renormalizable in low energy couplings.

Covariant regularization is essential for defining black hole entropy.

Effective field theory may explain black hole microstates and the information puzzle.

Abstract

We discuss the status of the black hole entropy formula $S_{\rm BH} = A_H /4G$ in low energy effective field theory. The low energy expansion of the black hole entropy is studied in a non-equilibrium 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 sphaleron-like 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 virtues of the use of covariant regularization prescriptions. In fact, the definition of black hole entropy in terms of decay rates {\it 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 quasi-coherent 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.