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

Abstract

Detailed observations of phenomena involving black holes, be it via gravitational waves or more traditional electromagnetic means, can probe the strong field regime of the gravitational interaction. The prediction of features in such observations requires detailed knowledge of the black hole spacetime, both within and outside of General Relativity. We present here a new numerical code that can be used to obtain stationary solutions that describe black hole spacetimes 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 by considering static and spherically symmetric black holes both in General Relativity, as well as in scalar-Gauss-Bonnet gravity with a linear (linear scalar-Gauss-Bonnet) and an exponential (Einstein-dilaton-Gauss-Bonnet) coupling. As a by-product 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. As expected, 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.

Gravitational Test beyond the First Post-Newtonian Order with the Shadow of the M87 Black Hole

“…[101] of Ref. [33], which is written in isotropic coordinates). Without loss of generality, we consider photon trajectories in the equatorial plane, i.e., set θ ¼ π=2.…”

Gravity with a generalized conformal scalar field: Theory and solutions

“…(33) This profile, when substituted in the Einstein equations (16), results in a set of modified Friedmann equations that take the remarkably simple form…”

“…However, modified theories with new fundamental fields typically present field equations with increased complexity such that these calculations become analytically impossible. One is then forced to resort either to perturbation theory, which is not well-justified in the extreme gravity regime, or to challenging numerical techniques [16]. * p.g.s.fernandes@qmul.ac.uk Nonetheless, the Einstein equations with a matter source possessing conformal invariance are greatly simplified since the theory has constant scalar curvature onshell, restricting the possible spacetimes and allowing for closed-form solutions to be easily found.…”

Black hole sensitivities in Einstein-scalar-Gauss-Bonnet gravity

“…They are a subclass of Horndeski gravity [18,19] and also arise from an effective field theory perspective [20,21]. Due to the coupling between the scalar field and the Gauss-Bonnet density, black holes in these theories can violate no-hair theorems [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37] and exhibit spontaneous scalarization [38][39][40][41][42]. As a consequence, black holes are endowed with a monopole scalar charge, which can source dipolar scalar radiation in binary black hole systems [43,44].…”