Analytically Approximation Solution to Higher Derivative Gravity

TL;DR

This paper develops an analytical approximation method to find black hole solutions in higher derivative gravity with electromagnetic sources, analyzing their thermodynamics and geodesics.

Contribution

It introduces a continued fraction method to derive approximate solutions for higher derivative gravity black holes, including thermodynamic and geodesic properties.

Findings

Derived approximate black hole solutions in higher derivative gravity.

Validated thermodynamic consistency with first law and Smarr formula.

Analyzed null and time-like geodesics around the black holes.

Abstract

We obtain analytical approximate black hole solutions for higher derivative gravity in the presence of Maxwell electromagnetic source. We construct near horizon and asymptotic solutions and then use these to obtain an approximate analytic solution using a continued fraction method to get a complete solution. We compute the thermodynamic quantities and check the first law and Smarr formula. Finally, we investigate the null and time-like geodesics of this black hole.