Eur.Phys.J.C, 84, 515 (2024)

Thermodynamics of Taub-NUT-AdS spacetimes

 Jun-Fei Liu¹ and Hai-Shan Liu^1,*

1 Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin university, Yaguan Road 135, Jinnan District, Tianjin 300350, China.

* hsliu.zju@gmail.com

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 NUT 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.