Revisiting mass formulas of the four-dimensional Reissner-Nordström-NUT-AdS solutions in a different metric form

Abstract

Recently, the so-called “consistent thermodynamics” of the Lorentzian Reissner-Nordström (RN)-NUT-AdS4 spacetimes has been pursued by a lot of efforts via different means. Among these attempts, we had proposed a novel idea that “The NUT charge is a thermodynamical multihair” to successfully tackle with the subject. In this paper, we will adopt this strategy to reconsider the mass formulas of the RN-NUT-AdS4 solutions but written in an alternative form, which had not been studied before in any existing literature and might be a most appropriate ansatz for the higher dimensional multiply NUTty-charged AdS spacetimes without any constraint condition. Here, we shall discuss the Christodoulou-Ruffini-like squared mass formula and the first law as well as the Bekenstein-Smarr mass formula by introducing the secondary hair Jn=Mn. For the sake of generality, we have introduced a dimensionless constant w into the constant factor Ξ in the solution expression so that when w=1, all obtained results can reproduce those delivered in our previous work.

Keywords

• Mass formulas
• Thermodynamics
• RN-NUT-AdS4
• Einstein- Maxwell theory