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.

• Received 10 December 2020
• Accepted 1 June 2021

DOI:https://doi.org/10.1103/PhysRevD.103.124058