Black hole binaries in cubic Horndeski theories

Numerical relativity for Horndeski gravity

“…5, for weakly-coupled solutions to the equations of motion, the structure of the equations of motion for the Horndeski are similar to the structure of the Einstein equations, and there exists several strongly hyperbolic formulations of the Horndeski equations of motion which have already been used in numerical relativity simulations of binary black hole spacetimes. 40,92,101 While the Horndeski theories have a well-posed initial value problem in this regime, there is no guaranteed that a given weakly-coupled solution will remain weakly coupled at later times. We first recall that solutions to GR can break down at spacetime singularities.…”

“…This being said, researchers have numerically evolved binary black hole spacetimes in quadratic Horndeski gravity, cubic Horndeski gravity, and in ESGB gravity (both theories which can form naked elliptic regions in gravitational collapse 26,[37][38][39]107 ) through merger, and have found sets of initial data that did not lead to the formation of a naked elliptic regions or shocks. 40,92,101 Numerical studies of the detailed PDE nonlinear properties of the Horndeski gravity theories have mostly been confined to spherically symmetric spacetimes. In Fig.…”

“…For more discussion see Ref. 123 coefficients inside the black hole horizon 39,92 (thus the theory in some sense adiabatically reduces to GR inside the black hole)-we note that the authors refer to this scheme also as a form of "excision". Sonic lines have been found in solutions to quadratic Horndeski gravity theories as well.…”

“…Figueras and França 39,92 have recently performed the first fully-nonlinear simulations of dynamical black hole spacetimes in a cubic Horndeski gravity theory. In both works, they considered couplings of the form G 2 = g 2 X 2 and G 3 = g 3 X, where g 2 and g 3 are constants, and either V = 0 39 or V = 1 2 m 2 φ 2 .…”

“…In both works, they considered couplings of the form G 2 = g 2 X 2 and G 3 = g 3 X, where g 2 and g 3 are constants, and either V = 0 39 or V = 1 2 m 2 φ 2 . 92 To evolve the equations of motion in well-posed fashion, the authors rewrote the equations of motion as described by Kovacs, 27 and then made use of the CCZ4 formulation 90,91 (see also Sec. 5.2).…”