Discussion of a possible corrected black hole entropy

TL;DR

This paper explores how black hole entropy may be corrected in Einstein and EiBI gravity theories, deriving the first law of thermodynamics for these models and proposing a specific corrected entropy formula.

Contribution

It introduces a generalized method to derive corrected black hole entropy in Einstein and EiBI gravity, including cases with electromagnetic fields.

Findings

Entropy correction in Einstein gravity derived from a generalized static spherically symmetric metric.

First law of thermodynamics established for EiBI gravity without matter.

A specific corrected entropy formula for black holes in EiBI gravity with electromagnetic fields.

Abstract

Einstein's equation could be interpreted as the first law of thermodynamic near the spherically symmetric horizon. Through recalling the Einstein gravity with a more general static spherical symmetric metric, we find that the entropy would have a correction in Einstein gravity. By using this method, we investigate the Eddington-inspired Born-Infeld (EiBI) gravity. Without matter field, we can also derive the first law in EiBI gravity. With an electromagnetic field, as the field equations have a more general spherically symmetric solution in EiBI gravity, we find that correction of the entropy could be generalized to EiBI gravity. Furthermore, we point out that the Einstein gravity and EiBI gravity might be equivalent on the event horizon. At last, under EiBI gravity with the electromagnetic field, a specific corrected entropy of black hole is given.