Thermodynamic Product Formula for Taub-NUT Black Hole

TL;DR

This paper explores the thermodynamic properties of Taub-NUT black holes, deriving relations for their horizons, analyzing stability, and comparing with Reissner-Nordström black holes to understand entropy at microscopic levels.

Contribution

It introduces new thermodynamic relations for Taub-NUT black holes and analyzes their stability, highlighting non-universality of certain horizon properties.

Findings

Area product, sum, difference, and division are not universal.

Black holes are thermodynamically unstable due to negative specific heat.

Derived bounds on area, entropy, and irreducible mass for horizons.

Abstract

We derive various important thermodynamic relations of the inner and outer horizon in the background of Taub-NUT(Newman-Unti-Tamburino) black hole in four dimensional \emph{Lorentzian geometry}. We compare these properties with the properties of Reissner Nordstr{\o}m black hole. We compute \emph{area product, area sum, area minus and area division} of black hole horizons. We show that they all are not universal quantities. Based on these relations, we compute the area bound of all horizons. From area bound, we derive entropy bound and irreducible mass bound for both the horizons. We further study the stability of such black hole by computing the specific heat for both the horizons. It is shown that due to negative specific heat the black hole is thermodynamically unstable. All these calculations might be helpful to understanding the nature of black hole entropy both \emph{interior} and exterior at the microscopic level.