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

Shuang-Qing Wu; Di Wu

doi:10.1103/PhysRevD.100.101501

paper

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

arXiv:1909.07776 · doi:10.1103/PhysRevD.100.101501

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 ( $M = m$ ), the "angular momentum" ( $J_{n} = mn$ ), the gravitomagnetic charge ( $N = n$ ), and/or the dual (magnetic) mass ( $M = n$ ). 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 four-dimensional 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.

7 pages, twocolumn, revtex4-1. Matched with published version; Ref.[32] is contained in the source file of 1909.07776v1

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

Abstract

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