Taub-NUT Black Hole in Higher Derivative Gravity and Its Thermodynamics

TL;DR

This paper develops first-order perturbative solutions for Taub-NUT black holes in higher derivative gravity, analyzes their thermodynamics, and verifies the applicability of the Reall-Santos method beyond asymptotic flatness.

Contribution

It introduces the first perturbative Taub-NUT solutions in cubic curvature extended Einstein gravity and applies the Reall-Santos method to study their thermodynamics.

Findings

Thermodynamic quantities corrected at first order in perturbation

First law and Smarr relation verified for corrected solutions

Reall-Santos method applicable beyond asymptotic flatness

Abstract

We construct the first-order perturbative Taub-NUT black hole solutions in Einstein gravity extended with a cubic curvature invariant. The corrected thermodynamic quantities are then obtained by the standard method and the first law and Smarr relation are satisfied. We also study the perturbative correction to thermodynamics using the Reall-Santos (RS) method and verify that the method is still applicable even though the metrics are no longer asymptotic to Minkowski spacetime. We then apply the RS method to obtain the leading correction to the thermodynamics of the complicated Kerr-Taub-NUT black holes.