Numerical relativity for Horndeski gravity

TL;DR

This paper reviews recent advances in numerical methods for solving Horndeski gravity theories, focusing on well-posed formulations, global solution behaviors, and numerical simulations of compact binary systems.

Contribution

It provides a comprehensive overview of numerical approaches, well-posedness issues, and global solution phenomena in Horndeski gravity, including binary system simulations.

Findings

Well-posed formulations for Horndeski theories established

Global behaviors like shock formation and singularities analyzed

Numerical simulations of binary black holes and neutron stars conducted

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.