One-loop Renormalization of Black Hole Entropy Due to Non-minimally Coupled Matter

TL;DR

This paper investigates how quantum entanglement entropy of black holes is affected by non-minimally coupled matter, demonstrating that divergences can be renormalized through gravitational couplings, linking entanglement and thermodynamic entropy.

Contribution

It provides a one-loop renormalization analysis of black hole entropy for non-minimally coupled scalar fields using Euclidean path integrals on $oldsymbol{eta}$-fold coverings.

Findings

Divergences in entanglement entropy are renormalized by gravitational couplings.

The relationship between entanglement and thermodynamical entropy is clarified.

The approach applies to non-minimally coupled scalar matter.

Abstract

The quantum entanglement entropy of an eternal black hole is studied. We argue that the relevant Euclidean path integral is taken over fields defined on $\alpha$-fold covering of the black hole instanton. The statement that divergences of the entropy are renormalized by renormalization of gravitational couplings in the effective action is proved for non-minimally coupled scalar matter. The relationship of entanglement and thermodynamical entropies is discussed.