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

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 $J=a\,M$.