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

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.

arXiv comment24 pages, 7 figures

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• Thermodynamics of Dyonic NUT Charged Black Holes with Entropy as Noether Charge
• Consistent mass formulas for higher even-dimensional Taub-NUT spacetimes and their AdS counterparts
• Charging Kerr-Schild spacetimes in higher dimensions
• Thermodynamics of Taub-NUT/Bolt-AdS Black Holes in Einstein-Gauss-Bonnet Gravity
• Consistent mass formulas for higher even-dimensional Reissner-Nordström-NUT-AdS spacetimes
• Topological Characterization of Higher Dimensional Charged Taub-NUT Instantons
• Thermodynamic studies of Different Type of Black Holes: General Uncertainty Principle Approach
• Einstein-Born-Infeld on Taub-NUT Spacetime in 2k+2 Dimensions
• Higher-Curvature Gravity, Black Holes and Holography
• Embedding diagrams in stationary spacetimes
• Entropy Product Formula for Gravitational Instanton
• Thermodynamics and Phase Transitions of NUTty Dyons