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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.
Sullivan et al. (Fri,) studied this question.