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

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.

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

“…N (1) = 0, Φ(1) = Φ H and Φ (1) = −x + (x 2 − 3/2) 1/2 where x = 2e −2Φ H − 1/2, and note that Φ H is the only integration constant. The latter can finally be traded (36) as functions of the quantity φ + ln( /µ) introduced in Eq. (39).…”

“…( 29) and below Eq. (36). For the Gaussian theory we choose ϕ 0 = 0, which corresponds to a nondynamical scalar field on cosmological scales, at least classically [91].…”

“…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].…”

“…FIG.5. Black hole mass and sensitivity in the dilatonic theory(36) as functions of the quantity φ + ln( /µ) introduced in Eq (39)…”

New Horizons for Fundamental Physics with LISA

“…This is important, because NR and recent GW observations indicate that the spin of the merger remnant is generally large (Abbott et al, 2019b;Berti and Volonteri, 2008;Berti et al, 2007;Buonanno et al, 2007;Hofmann et al, 2016). Unfortunately most rotating BH solutions beyond GR are only known either perturbatively, as small-spin expansion around non-spinning backgrounds (Ayzenberg and Yunes, 2014;Cano and Ruipérez, 2019;Cardoso et al, 2018b;Maselli et al, 2015;Pani et al, 2011b), or they are given in the form of fully numerical solutions of the field equations (Cunha et al, 2019;Herdeiro et al, 2016;Kleihaus et al, 2011;Sullivan et al, 2020Sullivan et al, , 2021, which makes the application of perturbation theory difficult.…”