Energy Distribution of a Charged Black Hole with a Minimally Coupled Scalar Field

TL;DR

This paper calculates the energy distribution of a charged black hole with a scalar field in an Anti-deSitter background using multiple energy-momentum complexes, demonstrating their consistency as localized energy measures.

Contribution

It applies three different energy-momentum complexes to a charged black hole with a scalar field, showing their agreement and validating their use for localized energy calculations.

Findings

Consistent energy values across Einstein, Landau-Lifshitz, and Papapetrou complexes.

The metric belongs to the Kerr-Schild class.

The solution is asymptotically Anti-deSitter.

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.