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

• Published in: arXiv.org
• Main Authors: Wu, Di, Wu, Shuang-Qing
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 12.10.2023
• Subjects: Spacetime
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2210.17504

Recently, the so-called ``consistent thermodynamics'' of the Lorentzian Reissner-Nordstr\"{o}m (RN)-NUT-AdS\(_4\) 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-AdS\(_4\) 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 \(J_n = Mn\). For the sake of generality, we have introduced a dimensionless constant \(w\) into the constant factor \(\Xi\) in the solution expression so that when \(w = 1\), all obtained results can reproduce those delivered in our previous work.