Energy-Momentum Distribution in General Relativity for a Phantom Black Hole Metric

Abstract

We use the M{\o}ller and Landau-Lifshitz energy-momentum definitions in General Relativity (GR) to evaluate the energy-momentum distribution of the phantom black hole space-time. The phantom black hole model was applied to the supermassive black hole at the Galactic Centre. We obtain that in both pseudotensorial prescriptions the energy distribution depends on the mass $M$ of the black hole, the phantom constant $p$ and the radial coordinate $r$. Further, all the calculated momenta are found to be zero. The limiting cases $r\rightarrow 0$, $r\rightarrow \infty $ and $r\rightarrow -\infty $ have also been the subject of the study.