General Relativity and Gravitation ( IF 2.8 ) Pub Date : 2021-07-17 , DOI: 10.1007/s10714-021-02836-w Parthapratim Pradhan 1
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 \(J=a\,M\).
中文翻译:
Newman-Unti-Tamburino 类黑洞的能量公式
我们计算表面能 (\(\mathcal{E}_{s}^{\pm }\))、旋转能 (\(\mathcal{E}_{r}^{\pm }\))和具有事件视界 ( \(\mathcal{H}^{ ) 的 Newman-Unti-Tamburino (NUT) 类黑洞的电磁能 ( \(\mathcal{E}_{em}^{\pm }\) +}\))和柯西视界(\(\mathcal{H}^{-}\))。值得注意的是,我们发现质量参数可以表示为三个能量的总和,即 \(M=\mathcal{E}_{s}^{\pm }+\mathcal{E}_{r}^{\pm } +\mathcal{E}_{em}^{\pm }\)。已经测试过了Taub-NUT 黑洞、Reissner-Nordström-Taub-NUT 黑洞、Kerr-Taub-NUT 黑洞和 Kerr-Newman-Taub-NUT 黑洞。在黑洞的每种情况下,我们发现这些能量的总和等于 Komar 质量。仅由于引入了新的守恒电荷,即\(J_{N}=M\,N\) (其中\(M=m\)是 Komar 质量,\(N=n\)是引力磁电荷),这与类克尔角动量参数\(J=a\,M\)非常相似。