Black hole entropy arising from massless scalar field with Lorentz violation induced by the coupling to Einstein tensor

TL;DR

This paper studies how a massless scalar field with Lorentz violation, coupled to Einstein tensor, affects black hole entropy, revealing that the entropy depends on the coupling and effective metric, not just the horizon area.

Contribution

It introduces a novel analysis of black hole entropy considering Lorentz violation from scalar field coupling, showing the entropy's dependence on the effective metric and coupling parameters.

Findings

Scalar field contributes to the classical Bekenstein-Hawking entropy.

Entropy depends on the effective metric related to the coupling.

Classical entropy is not simply proportional to the horizon area.

Abstract

We have investigated quantum entropy of a static black hole arising from the massless scalar field with Lorentz violation induced by the coupling to Einstein tensor. Our results show that the coupled massless scalar field contributes to the classical Bekenstein-Hawking term in the black hole entropy. The corrected classical Bekenstein-Hawking entropy is not one quarter of the event horizon area of the original background black hole, but of a corresponding effective metric related to the coupling. It means that the classical Bekenstein-Hawking entropy depends not only on the black hole parameter, but also on the coupling which reduces Lorentz violation.