Higher dimensional black holes with a generalized gravitational action

TL;DR

This paper investigates how higher order curvature corrections in a general gravitational action affect static, spherically symmetric black holes in higher dimensions, focusing on horizon properties, temperature, and entropy calculations.

Contribution

It introduces a perturbative method to analyze the impact of fourth and sixth order curvature invariants on black hole solutions and thermodynamics in higher dimensions.

Findings

Corrections modify the event horizon location, temperature, and entropy.

Entropy calculations agree with the first law of thermodynamics.

Lovelock combinations yield exact entropy expressions.

Abstract

We consider the most general higher order corrections to the pure gravity action in $D$ dimensions constructed from the basis of the curvature monomial invariants of order 4 and 6, and degree 2 and 3, respectively. Perturbatively solving the resulting sixth-order equations we analyze the influence of the corrections upon a static and spherically symmetric back hole. Treating the total mass of the system as the boundary condition we calculate location of the event horizon, modifications to its temperature and the entropy. The entropy is calculated by integrating the local geometric term constructed from the derivative of the Lagrangian with respect to the Riemann tensor over a spacelike section of the event horizon. It is demonstrated that identical result can be obtained by integration of the first law of the black hole thermodynamics with a suitable choice of the integration constant. We show that reducing coefficients to the Lovelock combination, the approximate expression describing entropy becomes exact. Finally, we briefly discuss the problem of field redefinition and analyze consequences of a different choice of the boundary conditions in which the integration constant is related to the exact location of the event horizon and thus to the horizon defined mass.