Well-posedness of the four-derivative scalar-tensor theory of gravity in singularity avoiding coordinates

TL;DR

This paper establishes the well-posedness of a general four-derivative scalar-tensor gravity theory in singularity-avoiding coordinates and demonstrates its practical robustness through black hole merger simulations.

Contribution

It introduces a modified CCZ4 formulation for scalar-tensor theories, enabling stable numerical simulations with larger coupling constants.

Findings

The formulation is well-posed for small couplings.

Simulations remain stable with larger, order-one couplings.

The work facilitates numerical relativity studies of advanced gravity theories.

Abstract

We show that the most general scalar-tensor theory of gravity up to four derivatives in $3+1$ dimensions is well-posed in a modified version of the CCZ4 formulation of the Einstein equations in singularity-avoiding coordinates. We demonstrate the robustness of our new formulation in practise by studying equal mass black hole binary mergers for different values of the coupling constants. Although our analysis of well-posedness is restricted to cases in which the couplings are small, we find that in simulations we are able to push the couplings to larger values, so that a certain weak coupling condition is order one, without instabilities developing. Our work provides the means for such simulations to be undertaken by the many numerical relativity codes that rely on the moving puncture gauge to evolve black hole singularities.