Thermodynamics of Taub-NUT Black Holes in Einstein-Maxwell Gravity

TL;DR

This paper constructs and analyzes the thermodynamics of Taub-NUT and bolt solutions in higher-dimensional Einstein-Maxwell gravity, revealing stability conditions and phase behaviors dependent on dimensionality and electric potential.

Contribution

It introduces new higher-dimensional Taub-NUT/bolt solutions with electric charge and potential, and examines their thermodynamic stability and phase structure.

Findings

NUT solutions have no curvature singularity at r=N for base space $ ext{CP}^{2k}$.

Thermodynamic quantities satisfy the first law of black hole thermodynamics.

NUT solutions are thermally unstable for even dimensions, stable for odd dimensions.

Abstract

First, we construct the Taub-NUT/bolt solutions of $(2k+2)$-dimensinal Einstein-Maxwell gravity, when all the factor spaces of $2k$-dimensional base space $\mathcal{B}$ have positive curvature. These solutions depend on two extra parameters, other than the mass and the NUT charge. These are electric charge $q$ and electric potential at infinity $V$. We investigate the existence of Taub-NUT solutions and find that in addition to the two conditions of uncharged NUT solutions, there exist two extra conditions. These two extra conditions come from the regularity of vector potential at $r=N$ and the fact that the horizon at $r=N$ should be the outer horizon of the NUT charged black hole. We find that the NUT solutions in $2k+2$ dimensions have no curvature singularity at $r=N$, when the $2k$-dimensional base space is chosen to be $\mathbb{CP}^{2k}$. For bolt solutions, there exists an upper limit for the NUT parameter which decreases as the potential parameter increases. Second, we study the thermodynamics of these spacetimes. We compute temperature, entropy, charge, electric potential, action and mass of the black hole solutions, and find that these quantities satisfy the first law of thermodynamics. We perform a stability analysis by computing the heat capacity, and show that the NUT solutions are not thermally stable for even $k$'s, while there exists a stable phase for odd $k$'s, which becomes increasingly narrow with increasing dimensionality and wide with increasing $V$. We also study the phase behavior of the 4 and 6 dimensional bolt solutions in canonical ensemble and find that these solutions have a stable phase, which becomes smaller as $V$ increases.