Thermodynamics of $(d+1)$-dimensional NUT-charged AdS Spacetimes

TL;DR

This paper investigates the thermodynamic properties of higher-dimensional NUT-charged AdS spacetimes, revealing stability conditions and extending results across various dimensions using advanced computational methods.

Contribution

It provides a comprehensive analysis of thermodynamics in $(d+1)$-dimensional NUT-charged AdS spacetimes, including stability criteria and generalization to arbitrary dimensions.

Findings

Pure NUTs in $4k+2$ dimensions are thermodynamically unstable.

Stable regions exist for NUTs in $4k$ dimensions, decreasing with higher dimensions.

Bolt solutions exhibit regions of thermodynamic stability.

Abstract

We consider the thermodynamic properties of $(d+1)$-dimensional spacetimes with NUT charges. Such spacetimes are asymptotically locally anti de Sitter (or flat), with non-trivial topology in their spatial sections, and can have fixed point sets of the Euclidean time symmetry that are either $(d-1)$-dimensional (called "bolts") or of lower dimensionality (pure "NUTs"). We compute the free energy, conserved mass, and entropy for 4, 6, 8 and 10 dimensions for each, using both Noether charge methods and the AdS/CFT-inspired counterterm approach. We then generalize these results to arbitrary dimensionality. We find in $4k+2$ dimensions that there are no regions in parameter space in the pure NUT case for which the entropy and specific heat are both positive, and so all such spacetimes are thermodynamically unstable. For the pure NUT case in $4k$ dimensions a region of stability exists in parameter space that decreases in size with increasing dimensionality. All bolt cases have some region of parameter space for which thermodynamic stability can be realized.