Abstract
In this paper, we investigate the thermodynamics of the charged NUT black hole with the Misner strings present in the Einstein-Maxwell gravity. We show that the Misner charge $N$ can be obtained by performing Komar integration over the Misner strings in the presence of electric and magnetic charges and the corresponding Smarr relation and first law can also be naturally established based on this geometric perspective. Besides, we demonstrate that the electric and magnetic charges appearing in the first law and Smarr relation are contingent on the special choice of gauge freedom for the electric and magnetic potentials. We re-derive two different versions of thermodynamics according to distinct choices of gauge and furthermore, we try to formulate more general thermodynamic laws under other arbitrary choices of gauge and deduce the conditions necessary to satisfy the Smarr relations and first laws simultaneously.
Highlights
As one of the most interesting solutions of general relativity, the Taub-NUT (Newman-Unti-Tamburino) spacetime [1,2] has engendered lots of perplexing problems since its birth
As shown by some recent studies [9,10,11], the Taub-NUT solution in the Lorentzian setup does not lead to serious problems as imagined previously, and when establishing the Smarr relation and first law of thermodynamics, the core ingredient is to introduce a pair of novel conjugate thermodynamic quantities, namely, the Misner potential and charge ψ–N [12,16] to ensure that the NUT parameter n varies independently
Inspired by the uncharged case [16] and the solution with rotation [22], in this paper we have reformulated the thermodynamic laws of the charged NUT black hole with the Misner strings present in the Einstein-Maxwell gravity from the Komar integral perspective, and shown that the Misner charges in this case are corresponding to Komar integrals over the Misner strings
Summary
As one of the most interesting solutions of general relativity, the Taub-NUT (Newman-Unti-Tamburino) spacetime [1,2] has engendered lots of perplexing problems since its birth. This manipulation brings about many new problems It leads to the existence of closed timelike curves everywhere and makes the spacetime geodesically incomplete [3,4,5] and when establishing thermodynamics of this spacetime, the NUT parameter n is no longer a valid independent variable but rather a function of the Schwarzschild-like horizon radius rh due to the identification between the standard temperature formula and the reciprocal of the periodicity of the Euclidean time coordinate [6].
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