Perturbative Metric of Charged Black Holes in Quadratic Gravity

TL;DR

This paper derives third-order perturbative corrections to charged black hole metrics in quadratic gravity, analyzing their thermodynamics and showing deviations from standard entropy-area relations.

Contribution

It provides explicit third-order corrections to Reissner–Nordström black holes within quadratic gravity and explores their thermodynamic properties.

Findings

Corrections to black hole metrics up to third order in coupling constant.

Modified temperature and entropy-area relations for charged black holes.

Deviations from the standard Bekenstein-Hawking entropy formula.

Abstract

We consider perturbative solutions to the classical field equations coming from a quadratic gravitational lagrangian in four dimensions. We study the charged, spherically symmetric black hole and explicitly give corrections up to third order (in the coupling constant $\beta$ multiplying the $R_{\mu\nu}R^{\mu\nu}$ term) to the Reissner--Nordstr\"om hole metric. We consider the thermodynamics of such black holes, in particular, we compute explicitly its temperature and entropy--area relation which deviates from the usual $S=A/4$ expression.