Multihair thermodynamics of Kerr-Newman-NUT-AdS${}_4$ spacetimes

Abstract

In this paper, we develop a multihair thermodynamic description of Lorentzian Kerr-Newman-NUT-AdS${}_4$ spacetime in which rotation, electric charge, AdS pressure and polar conical tensions enter a homogeneous Christodoulou-Ruffini-type squared-mass formula. The NUT contribution is described by a rotation-like secondary hair $J_n=mn/K^2$ and a charge-like secondary hair $N=n/\sqrt{K}$. Both depend on the metric parameters of the physical solution family but are varied independently in the enlarged thermodynamic state space. The mass formula yields the first law and Smarr relation in a single enthalpy representation, with the area entropy and Hawking temperature. The Kerr-Newman-AdS, asymptotically flat Kerr-Newman-NUT and nonrotating RN-NUT-AdS limits check the angular normalization and the NUT and pressure contributions. We also consider alternative NUT variables, including the conformal dual mass, and derive the corresponding changes in thermodynamic volume and conical-defect lengths. This description applies to the chosen homogeneous state space and does not require the secondary hairs to be independent asymptotic or Misner-string surface charges.

11 pages, 2 tables