Energy formula for Newman-Unti-Tamburino class of black holes

Abstract

We compute the surface energy ($\mathcal{E}_{s}^{\pm }$), the rotational energy ($\mathcal{E}_{r}^{\pm }$) and the electromagnetic energy ($\mathcal{E}_{em}^{\pm }$) for Newman-Unti-Tamburino (NUT) class of black hole having the event horizon ($\mathcal{H}^{+}$) and the Cauchy horizon ($\mathcal{H}^{-}$). Remarkably, we find that the mass parameter can be expressed as sum of three energies i.e. $M=\mathcal{E}_{s}^{\pm }+\mathcal{E}_{r}^{\pm }+\mathcal{E}_{em}^{\pm }$. It has been tested for Taub-NUT black hole, Reissner-Nordström-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 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 $J=a\,M$.