Energy distribution of a charged black hole with a minimally coupled scalar field

Abstract

Using three different energy-momentum complexes, the Einstein, Landau-Lifshitz, and Papapetrou prescriptions, we calculate the energy of an electrically charged black hole exact solution with a self-interacting, minimally-coupled scalar field and the asymptotic region locally an anti-deSitter spacetime. Writing the metric in Kerr-Schild Cartesian coordinates, we demonstrate that this metric belongs to the Kerr-Schild class of solutions. Applying each of the three energy-momentum prescriptions and comparing the results, we find consistency among these complexes, suggesting their utility as localized measures of energy.

Black Plane Solutions and Localized Gravitational Energy

“…Xulu has examined the Møller energy of nonstatic, spherically symmetric spacetimes [ 22 ]. Halpern has investigated the energy distribution of a charged black hole with a minimally coupled scalar field [ 23 ] and, along with Pecorino, a static, electrically neutral, spherically symmetric massive body embedded in a space filled with phantom energy [ 24 ].…”

The Localized Energy Distribution of Dark Energy Star Solutions

“…Sharif has examined the energy of rotating spacetimes in teleparallel gravity (Sharif and Jawad 2011). Halpern has investigated the energy distribution of a charged black hole with a minimally coupled scalar field (Halpern 2008).…”