Energy associated with charged dilaton black holes

TL;DR

This paper investigates the energy distribution of charged dilaton black holes, revealing how it varies with the coupling parameter and radial distance, while total energy remains constant across different couplings.

Contribution

It derives the energy associated with static charged dilaton black holes for any coupling parameter, highlighting the dependence of energy distribution on this parameter.

Findings

Energy distribution varies with the coupling parameter β.

Total energy is invariant across all values of β.

Energy increases, decreases, or remains constant depending on β and radial distance.

Abstract

It is known that certain properties of charged dilaton black holes depend on a free parameter $\beta$ which controls the strength of the coupling of the dilaton to the Maxwell field. We obtain the energy associated with static spherically symmetric charged dilaton black holes for arbitrary value of the coupling parameter and find that the energy distribution depends on the value of $\beta$. With increasing radial distance, the energy in a sphere increases for $\beta = 0$ as well as for $\beta < 1$, decreases for $\beta > 1$, and remains constant for $\beta = 1$. However, the total energy turns out to be the same for all values of $\beta$.