Finite Entanglement Entropy of Black Holes

TL;DR

This paper demonstrates that in certain super-renormalizable gravity theories, the entanglement entropy of black holes is finite, positive, gauge-independent, and coincides with the classical Bekenstein-Hawking entropy, due to vanishing beta functions.

Contribution

It explicitly proves the vanishing of all beta functions except the cosmological constant in specific gravity theories, ensuring finite, physical black hole entropy via conical entropy.

Findings

Beta functions vanish except for the cosmological constant.

Conical entropy is finite, positive, and gauge-independent.

Conical entropy matches Bekenstein-Hawking entropy.

Abstract

We compute the area term contribution to black holes' entanglement entropy (using the conical technique) for a class of local or weakly non-local super-renormalizable gravitational theories coupled to matter. For the first time, we explicitly prove that all the beta functions in the proposed theory, except for the cosmological constant, are identically zero in cut-off regularization scheme and not only in dimensional regularization scheme. In particular, we show that there is no divergence quadratic in cut-off and hence there is no contribution to the beta function of the Newton constant. As a consequence of this result, we argue that in these theories of gravity conical entropy is a sensible definition of physical entropy, in particular, it is positive-definite and gauge-independent. On top of this the conical entropy, being expressed only in terms of the classical Newton constant, turns out to be finite and naturally coincides with Bekenstein-Hawking entropy. Finally, we propose a theory in which the renormalization of the Newton constant is entirely due to the Standard Model matter, arguing that such a contribution does not give the usual interpretational problems of conical entropy discussed in the literature.