Thermodynamics of Taub-NUT-AdS Spactimes

TL;DR

This paper applies a generalized Komar method to compute thermodynamic quantities of Taub-NUT-AdS spacetimes in Einstein gravity, confirming the first law and Smarr relation, and extends the approach to charged NUTy spacetimes in Einstein-Maxwell theory.

Contribution

It demonstrates the effectiveness of a generalized Komar method in deriving thermodynamic properties of Taub-NUT-AdS and charged NUTy spacetimes, confirming key thermodynamic relations.

Findings

Successfully derived mass and NUT charge using the generalized Komar method.

Confirmed the first law and Smarr relation for Taub-NUT-AdS spacetime.

Extended the method to charged NUTy spacetimes, verifying thermodynamic consistency.

Abstract

We apply the generalised Komar method proposed in [arxiv:2208.05494] to Taub-NUT-AdS spacetime in the theory of Einstein gravity plus a cosmological constant. Based on a generalised closed 2-form, we derive the total mass and NUT charge of the Taub-NUT-AdS spacetime. Together with other thermodynamic quantities calculated through standard method, we conform the first law and Smarr relation. Then, we consider charged AdS NUTy spacetimes in Einstein-Maxwell theory with a cosmological constant, and show that the generalised Komar method works, too. We obtain all the thermodynamic quantities, and the first law and Smarr relation are checked to be satisfied automatically.