Misner gravitational charges and variable string strengths

Abstract

As shown recently [1], consistent thermodynamics of the Lorentzian Taub-NUT solutions with Misner strings present can be formulated provided a new pair of conjugate quantities (related to the NUT parameter) ψ − N is introduced. In [1] this pair was calculated from the Euclidean action but no geometrical interpretation for the new quantities was provided. In this paper we propose that the potential ψ should be identified with the surface gravity of the Misner string and the conjugate Misner charge N can be obtained by a Komar-type integration over the tubes surrounding the string singularities. We show that similar tube contributions also modify the Komar formula for the thermodynamic volume. To render the integrals finite we employ the method of Killing copotentials. By construction the new charges then satisfy the Smarr relation. Equipped with these geometrical notions, we generalize the first law for the (possibly charged) Taub-NUT spacetimes to account for asymmetric distributions of Misner strings and their potential variable strengths.

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.…”

“…Kerr-Taub-NUT boundaries: Misner turbes[44]. Apart from the standard boundary the event horizon H and spatial infinity Σ∞ , Kerr-Taub-NUT space-time has two Misner tubes T± located at north and south pole.…”

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

“…In [20], the authors gave the consistent first law and Smarr relation of the Nutty dyonic black hole containing the electric and magnetic charges based on the thermodynamic consideration. Inspired by the uncharged case [16] and Taub-NUT solution with rotation [22], in this section we would like to derive a general Smarr relation and then apply it to reexpress the thermodynamic quantities obtained in [20] from the Komar integral perspective. The key point to achieve it is the decomposition of the mass [23].…”

“…And this can be understood since the cosmological constant can be induced from a totally antisymmetric tensor field sourced by a membrane [13,14]. Originally, they just obtained the free energy by calculating Euclidean action [15] to identify the several thermodynamic terms and further determined the Misner charge N. Later, geometrical interpretation on the two novel quantities ψ and N was assigned [16] and it was shown that the Misner potential is exactly the surface gravity of the Misner strings and the Misner charge just corresponds to the Komar integration over the tubes surrounding the Misner strings. However, when extended to the charged Taub-NUT-AdS spacetime in the Einstein-Maxwell gravity [17][18][19], in this case the electric and magnetic charges which were called "Nutty dyon" both exist and the magnitudes of them depend on the radius of the 2-dimensional sphere (see (11) below).…”