Numerical Black Hole Solutions in Modified Gravity Theories: Axial Symmetry Case

TL;DR

This paper develops a numerical method to find rotating black hole solutions in modified gravity theories, validating it in General Relativity and applying it to scalar-Gauss-Bonnet gravity to explore observable properties.

Contribution

The authors extend a numerical code to compute stationary, axisymmetric black hole solutions in various modified gravity theories, including scalar-Gauss-Bonnet gravity, and compare results with analytical solutions.

Findings

Successfully obtained rotating black hole solutions in scalar-Gauss-Bonnet gravity.

Validated the numerical code against known solutions in General Relativity.

Constructed an analytical model from numerical data to study observable properties.

Abstract

We extend a recently developed numerical code to obtain stationary, axisymmetric solutions that describe rotating black hole spacetimes in a wide class of modified theories of gravity. The code utilizes a relaxed Newton-Raphson method to solve the full nonlinear modified Einstein's Equations on a two-dimensional grid with a Newton polynomial finite difference scheme. We validate this code by considering static and axisymmetric black holes in General Relativity. We obtain rotating black hole solutions in scalar-Gauss-Bonnet gravity with a linear (linear scalar-Gauss-Bonnet) and an exponential (Einstein-dilaton-Gauss-Bonnet) coupling and compare them to analytical and numerical perturbative solutions. From these numerical solutions, we construct a fitted analytical model and study observable properties calculated from the numerical results.