Numerical black hole solutions in modified gravity theories: Axial symmetry case

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