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

TL;DR

This work extends the thermodynamic analysis of NUT-charged spacetimes to $(d+1)$ dimensions, contrasting Noether-charge and counterterm methods to compute action, mass, entropy, and specific heat for Taub-NUT–AdS and Taub-Bolt–AdS solutions across $d=3,5,7,9$ (dimensions 4,6,8,10). A key finding is the alternating stability pattern: in dimensions $4k$ there exists a finite NUT stability window, while in dimensions $4k+2$ pure NUT spacetimes are thermodynamically unstable; bolts, by contrast, always exhibit some stable region. The results show complete agreement between the Noether and counterterm approaches (up to a constant fixed by ground-state normalization) and provide general expressions for the NUT/Bolt action, mass, entropy, and specific heat in arbitrary even dimensions, with explicit analyses up to 10 dimensions. The study has implications for higher-dimensional gravity and holographic thermodynamics, highlighting how topological features and Misner strings influence gravitational entropy and 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.

Figures (11)

• Figure 4.1: Plot of the NUT Entropy and Specific Heat vs. $N$ in 6 dimensions
• Figure 4.2: Plot of Entropy and Specific Heat vs. $N$ for the upper branch Bolt solutions in 6 dimensions.
• Figure 4.3: Plot of lower branch Bolt Entropy vs. $N$ in 6 dimensions
• Figure 4.4: Plot of lower branch Bolt Specific Heat vs. $N$ in 6 dimensions
• Figure 5.1: Plot of NUT Entropy and Specific Heat vs. $N$ (8-dimensions)