Exact Black Hole Solutions in Modified Gravity Theories: Spherical Symmetry Case

We develop a numerical code that can solve for stationary and spherically symmetric spacetimes that represent black holes in a wide class of modified theories of gravity. The code makes use of a relaxed Newton-Raphson method to solve the discretized field equations with a Newton's polynomial finite difference scheme. We test and validate this code through studies both in General Relativity, as well as in Einstein-dilaton-Gauss-Bonnet gravity with a linear and an exponential coupling. As a byproduct of the latter, we find that analytic solutions obtained in the small coupling approximation are in excellent agreement with our fully non-linear solutions when using a linear coupling, although differences arise when using an exponential coupling. We then use these numerical solutions to construct a fitted analytical model which we then use to calculate physical observables such as the innermost stable circular orbit and photon sphere and compare them to the numerical results. This code lays the foundation for more detailed calculations of black hole observables that can be compared with data in the future.