Numerical relativity for Horndeski gravity

Abstract

We present an overview of recent developments in the numerical solution of Horndeski gravity theories, which are the class of all scalar-tensor theories of gravity that have second order equations of motion. We review several methods that have been used to establish well-posed initial value problems for these theories, and discuss well-posed formulations of the constraint equations. We also discuss global aspects of exact, strongly coupled solutions to some of Horndeski gravity theories: the formation of shocks, the loss of hyperbolicity, and the formation of naked curvature singularities. Finally we discuss numerical solutions to binary black hole and neutron star systems for several Horndeski theories.

Nonlinear studies of binary black hole mergers in Einstein-scalar-Gauss-Bonnet gravity

“…Here, we do not implement a method to solve the equations for general φ, but instead consider initial data for which φ = ∂ t φ = 0. With this choice of φ, the constraint equations of sGB gravity reduce to those of vacuum GR [22,23]. Even though φ = ∂ t φ =0 on the initial time slice, scalar field clouds subsequently form on a timescale that is short compared with the orbital binary timescale (within ∼ 100M 0 ).…”

“…After that initial evolution time, we turn on the Gauss-Bonnet coupling λ to a non-zero value. The constraints are satisfied in this procedure, as we can think of our initial data as starting at t = 50M 0 instead, with φ = ∂ t φ = 0 and a metric field that satisfies the constraints such that the initial data satisfies the constraint equations for sGB gravity [22,23]. While we use quasi-circular initial data based on PN approximations for the initial orbital velocities from GR, we found that the scalarization process does not appreciably impact the eccentricity of our runs, and instead the eccentricity of our runs is dominated by the truncation error of the simulations.…”

“…However, in order to seek physics beyond GR, or to place the most stringent constraints on deformations of GR, one needs accurate predictions for specific modified gravity theories, in particular in the strong field and dynamical regime [12][13][14][15]. This has been a major theoretical and technical challenge for many theories of interest [16][17][18][19][20][21][22][23][24][25]. As a result, most tests of GR performed so far are model-independent or null tests, more commonly classified as consistency and parametrized tests [4,[26][27][28][29].…”

“…Variants of ESGB gravity allow for scalar-charged black holes [30][31][32][33], and hence can differ qualitatively from GR in the strong field regime, while still passing weak field tests. Because of this, much recent work has gone into modeling compact object mergers in ESGB gravity in both post-Newtonian (PN) theory [34][35][36][37] and numerical relativity [19,22,23,[38][39][40]. In Ref.…”

“…In general, the equations of motion for ESGB gravity can only be stably evolved in time for weakly-coupled solutions [22,23,41,42,44]. Weak coupling roughly means that the Gauss-Bonnet corrections to the spacetime geometry remain sufficiently small compared to the smallest curvature length scale in the solution.…”