Energy Formula for Newman-Unti-Tamburino class of Black Holes

TL;DR

This paper derives an energy formula for NUT class black holes, expressing the mass as a sum of surface, rotational, and electromagnetic energies, confirmed across various black hole types, highlighting new conserved charges.

Contribution

It introduces a novel energy decomposition for NUT black holes, incorporating a new conserved charge, and verifies that the sum matches the Komar mass for multiple black hole solutions.

Findings

Mass equals sum of surface, rotational, and electromagnetic energies.

Sum of energies matches the Komar mass for tested black holes.

Introduction of new conserved charge J_N analogous to angular momentum.

Abstract

We compute the \emph{surface energy~(${\cal E}_{s}^{\pm}$), the rotational energy~(${\cal E}_{r}^{\pm}$) and the electromagnetic energy~(${\cal E}_{em}^{\pm}$)} for Newman-Unti-Tamburino~(NUT) class of black hole having the event horizon~(${\cal H}^{+}$) and the Cauchy horizon~(${\cal H}^{-}$). Remarkably, we find that the \emph{mass parameter can be expressed as sum of three energies i. e. $M={\cal E}_{s}^{\pm}+{\cal E}_{r}^{\pm}+{\cal E}_{em}^{\pm}$}. It has been \emph{tested} for Taub-NUT black hole, Reissner-Nordstr\"{o}m-Taub-NUT black hole, Kerr-Taub-NUT black hole and Kerr-Newman-Taub-NUT black hole. In each case of black hole, we find that \emph{the sum of these energies is equal to the Komar mass}. It is plausible only due to the introduction of new conserved charges i.e. $J_{N}=M\,N$~(where $M=m$ is the Komar mass and $N=n$ is the gravitomagnetic charge), which is closely analogue to the Kerr-like angular momentum parameter $J=a\,M$.