General Smarr relation and first law of a NUT dyonic black hole

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.

Topological dyonic Taub-Bolt/NUT-AdS solutions: Thermodynamics and first law

“…which is a sign for the consistency of this approach. If we substitute with M = M −2NΦ N , our Smarr's relation is identical to the one obtained recently in [38] for the spherical Lorentzian Taub-Bolt case. It is interesting to see here that the electric charge that enter the first law is Q ∞ e but the magnetic charge is the full charge Q m .…”

Weak cosmic censorship conjecture for a Kerr-Taub-NUT black hole with a test scalar field and particle

“…The thermodynamics of black holes with NUT parameter have been investigated extensively [42][43][44][45][46]. The first law of thermodynamics for the Kerr-Taub-NUT black hole is [43]…”

“…Recently, black holes with NUT charge have attracted some interesting researches, such as gravitational lensing [40], thermodynamics and phase transition [41][42][43][44][45][46], strong cosmic censorship conjecture [47] and weak cosmic censorship conjecture [48]. In this paper, we investigate the validity of the weak cosmic censorship conjecture for Kerr-Taub-NUT black holes by considering scattering of a test massive scalar field and injection of a test particle, respectively.…”

How appropriate are the gravitational entropy proposals for traversable wormholes?

“…In both the cases they have obtained consistent thermodynamics with positive thermodynamic volume. More work have been done recently by several authors [34][35][36][37][38] on the various thermodynamic issues. Clement et.al.…”