Quasistationary hair for binary black hole initial data in scalar Gauss-Bonnet gravity

TL;DR

This paper develops a method to construct quasistationary initial data for black holes in scalar Gauss-Bonnet gravity, enabling more accurate and stable numerical simulations of such systems.

Contribution

It extends the conformal thin sandwich framework to generate smooth, constraint-satisfying initial data for black holes with scalar hair in scalar Gauss-Bonnet theory, including binary systems.

Findings

Successfully constructed quasistationary scalar hair configurations.

Demonstrated smooth extension of solutions across black hole horizons.

Showed scalar hair is affected by the presence of a companion black hole.

Abstract

Recent efforts to numerically simulate compact objects in alternative theories of gravity have largely focused on the time-evolution equations. Another critical aspect is the construction of constraint-satisfying initial data with precise control over the properties of the systems under consideration. Here, we augment the extended conformal thin sandwich framework to construct quasistationary initial data for black hole systems in scalar Gauss-Bonnet theory and numerically implement it in the open-source SpECTRE code. Despite the resulting elliptic system being singular at black hole horizons, we demonstrate how to construct numerical solutions that extend smoothly across the horizon. We obtain quasistationary scalar hair configurations in the test-field limit for black holes with linear/angular momentum as well as for black hole binaries. For isolated black holes, we explicitly show that the scalar profile obtained is stationary by evolving the system in time and compare against previous formulations of scalar Gauss-Bonnet initial data. In the case of the binary, we find that the scalar hair near the black holes can be markedly altered by the presence of the other black hole. The initial data constructed here enable targeted simulations in scalar Gauss-Bonnet simulations with reduced initial transients.