Evolution of Einstein-scalar-Gauss-Bonnet gravity using a modified harmonic formulation

TL;DR

This paper develops and applies a numerical method to simulate black hole mergers in Einstein-scalar-Gauss-Bonnet gravity, enabling exploration of strong-field deviations from general relativity and comparison with gravitational wave data.

Contribution

It introduces a modified harmonic formulation for stable, full numerical evolution of Einstein-scalar-Gauss-Bonnet gravity applicable to all Horndeski theories, including black hole mergers.

Findings

Successfully simulated scalar cloud formation around black holes.

Demonstrated stability of the method near hyperbolicity limits.

Predicted gravitational wave signatures with deviations from GR.

Abstract

We present numerical solutions of several spacetimes of physical interest, including binary black hole mergers, in shift-symmetric Einstein-scalar-Gauss-Bonnet (ESGB) gravity, and describe our methods for solving the full equations of motion, without approximation, for general spacetimes. While we concentrate on the specific example of shift-symmetric ESGB, our methods, which make use of a recently proposed modification to the generalized harmonic formulation, should be generally applicable to all Horndeski theories of gravity (including general relativity). We demonstrate that these methods can stably follow the formation of scalar clouds about initially vacuum non-spinning and spinning black holes for values of the Gauss-Bonnet coupling approaching the maximum value above which the hyperbolicity of the theory breaks down in spherical symmetry. We study the collision of black holes with scalar hair, finding that the theory remains hyperbolic in the spacetime region exterior to the black hole horizons in a similar regime, which includes cases where the deviations from general relativity in the gravitational radiation is appreciable. Finally, we demonstrate that these methods can be used to follow the inspiral and merger of binary black holes in full ESGB gravity. This allows for making predictions for Horndeski theories of gravity in the strong-field and non-perturbative regime, which can confronted with gravitational wave observations, and compared to approximate treatments of modifications to general relativity.