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.
Highlights
As we enter a new era of multi-messenger astrophysics, many new experiments will allow us to test Einstein’s theory of general relativity (GR) in the strong field regime [1–6]
We have presented here a numerical infrastructure to calculate the exterior spacetimes of rotating black holes in a wide class of modified theories of gravity
We have validated this infrastructure by obtaining the Kerr solutions in GR and by direct comparison with a rotating, weak-coupling perturbative numerical solution in scalar Gauss-Bonnet (sGB) gravity
Summary
As we enter a new era of multi-messenger astrophysics, many new experiments will allow us to test Einstein’s theory of general relativity (GR) in the strong field regime [1–6]. One wants to test whether GR predictions fit the data, and whether they do so better than potential alternatives This requires the study of compact objects in modified gravity, and in particular, the solution to the full field equations for realistic astrophysical black holes. We first validate our numerics by studying rotating black holes in GR and we directly compare the numerical result to the known Kerr solution After this validation, we construct stationary, axially symmetric black holes in scalar Gauss-Bonnet (sGB) gravity, a well-motivated modified theory [7–10] that is a member of the quadratic gravity class [1, 6, 11]. We will construct fully nonlinear solutions in linear sGB and EDGB gravity that describe stationary and axially symmetric black holes We will compare these solutions to perturbative ones found in a weak-coupling expansion α = α/ρ2H 1, where ρH the horizon radius. We will conclude with an analysis of the properties of some physical observables that can be calculated with our non-linear solutions and our analytic, closed-form approximations
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