Analytical approximations to charged black hole solutions in Einstein-Maxwell-Weyl gravity

TL;DR

This paper applies the Homotopy Analysis Method to derive accurate analytical approximations for charged black hole solutions in Einstein-Maxwell-Weyl gravity, demonstrating consistency with numerical results across the spacetime outside the event horizon.

Contribution

It introduces a novel application of HAM to Einstein-Weyl gravity with Maxwell fields, providing analytical solutions that match numerical data.

Findings

Analytical solutions are accurate outside the event horizon.

Solutions are consistent with numerical results.

HAM effectively approximates black hole metrics in modified gravity.

Abstract

The Homotopy Analysis Method (HAM) is a useful method to derive analytical approximate solutions of black holes in modified gravity theories. In this paper, we study the Einstein-Weyl gravity coupled with Maxwell field, and obtain analytical approximation solutions for charged black holes by using the HAM. It is found that the analytical approximate solutions are sufficiently accurate in the entire spacetime outside the black hole's event horizon, and also consistent with numerical ones for charged black holes in the Einstein-Maxwell-Weyl gravity.