Einstein gravity with Gauss-Bonnet entropic corrections

TL;DR

This paper explores a modified Einstein gravity model with Gauss-Bonnet entropic corrections, deriving black hole solutions, entropy modifications, and cosmological implications including regular solutions and phases of acceleration.

Contribution

It introduces a toy model incorporating quantum-inspired Gauss-Bonnet entropic terms into Einstein gravity, analyzing black hole solutions and cosmological dynamics.

Findings

Black hole entropy receives a logarithmic correction to the area law.

Modified Friedmann equations reproduce the first law with consistent entropy and energy.

The model yields regular cosmological solutions with acceleration and de Sitter phases.

Abstract

A toy model of Einstein gravity with a Gauss-Bonnet classically "entropic" term mimicking a quantum correction is considered. The static black hole solution due to Tomozawa is found and generalized with the inclusion of non trivial horizon topology, and its entropy evaluated deriving the first law by equations of motion. As a result the Bekenstein-Hawking area law turns to be corrected by a logarithmic area term. A Misner-Sharp expression for the mass of black hole is found. Within a Friedmann-Lema\^itre-Robertson-Walker (FLRW) cosmological setting, the model is used in order to derive modified Friedmann equations. Such new equations are shown to reproduce the first law with the same formal entropy and quasi local energy of the static case, but here within a FLRW space-time interpreted as a dynamical cosmological black hole. A detailed analysis of cosmological solutions is presented, and it is shown that the presence of the correction term provides regular solutions and interesting phases of acceleration and decelerations, as well as, with negligible matter, exact de Sitter solutions.