Thermodynamical hairs of the four-dimensional Taub-Newman-Unti-Tamburino spacetimes

Abstract

It is demonstrated that the generic four-dimensional Taub-Newman-Unti-Tamburino (Taub-NUT) spacetimes can be perfectly described in terms of three or four different kinds of thermodynamic hairs: the Komar mass (M ¼ m), the "angular momentum" (J n ¼ mn), the gravitomagnetic charge (N ¼ n), and/or the dual (magnetic) mass (M ¼ n). In other words, the NUT charge is a thermodynamic multihair which means that it simultaneously has both rotation-like and electromagnetic charge-like characteristics; this is in sharp contrast with the previous knowledge that it has only one physical feature, or that it is purely a single solution parameter. To arrive at this novel result, we put forward a simple, systematic way to investigate the consistent thermodynamic first law and Bekenstein-Smarr mass formulas of all fourdimensional spacetimes that contain a nonzero NUT charge, facilitated by first deriving a meaningful Christodoulou-Ruffini-type squared-mass formula. In this way, not only can the elegant Bekenstein-Hawking one-quarter area-entropy relation be naturally restored in the Lorentzian and Euclidian sectors of generic Taub-NUT-type spacetimes without imposing any constraint condition, but also the physical meaning of the NUT parameter as a poly-facet can be completely clarified in the thermodynamic sense for the first time.

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.…”

On the properties of a deformed extension of the NUT space-time

“…Another direction towards the interpretation of the NUT space-time comes from the analysis of its thermodynamic properties. In [36] it was shown that if the NUT parameter is interpreted as possessing simultaneously rotational and electromagnetic features then the thermodynamic equivalent of Bekenstein-Smarr formula follows naturally. Another famous solution of the above class is the ZV space-time describing the gravitational field outside a static deformed object [10,11].…”

“…a stationary solution that has been thoroughly investigated, is the so-called Newman-Unti-Tamburino (NUT) space-time [34], which, due to its peculiar properties, was at some point referred to as a 'counterexample to everything' [35]. However, arguments exist in support to the fact that the NUT solution could posses some physical validity and the NUT parameter could in fact be related to angular momentum (see for example [36]). Similarly to Kerr, the NUT space-time is fully characterized by two parameters, one related to the mass of the source, and the other, the so-called NUT parameter, related to the gravitomagnetic charge of the source.…”

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

“…Although our treatment and the one in [21] have the same general idea of introducing a pair of thermodynamical variables N − Φ N , which is a natural consequence of having independent r 0 and n, the two approaches are different in their mass and their first law looks different as we will see below. While preparing this work we found the appearance of another related paper [39] which introduces again the same general idea of adding extra thermodynamic pairs, but this time it adds two new charges n and m n to study the thermodynamics of Lorentzian Taub-Bolt and NUT solutions with spherical horizons. Although this work studies a different class of Taub-Bolt/NUT solutions with different signature which includes electrically charged Taub-Bolt solutions it did not include the dyonic solution we studied here.…”