Puncture gauge formulation for Einstein-Gauss-Bonnet gravity and four-derivative scalar-tensor theories in $d+1$ spacetime dimensions

TL;DR

This paper develops a new formulation for Einstein-Gauss-Bonnet and scalar-tensor theories in higher dimensions, demonstrating well-posedness and enabling numerical relativity simulations to study gravitational modifications and scalarisation effects post-merger.

Contribution

It introduces a modified CCZ4 formulation for higher-dimensional gravity theories, ensuring well-posedness and providing tools for numerical analysis of scalarisation phenomena.

Findings

Scalarisation occurs too late to affect gravitational waveforms unless parameters are finely tuned.

Increasing coupling to accelerate scalarisation risks breaking the effective field theory.

The formulation enables future numerical studies of modified gravity effects in gravitational wave signals.

Abstract

We develop a modified CCZ4 formulation of the Einstein equations in $d+1$ spacetime dimensions for general relativity plus a Gauss-Bonnet term, as well as for the most general parity-invariant scalar-tensor theory of gravity up to four derivatives. We demonstrate well-posedness for both theories and provide full expressions for their implementation in numerical relativity codes. As a proof of concept, we study the so-called ``stealth-scalarisation'' induced by the spin of the remnant black hole after merger. As in previous studies using alternative gauges we find that the scalarisation occurs too late after merger to impact on the tensor waveform, unless the parameters are finely tuned. Naively increasing the coupling to accelerate the growth of the scalar field risks a breakdown of the effective field theory, and therefore well-posedness, as the evolution is pushed into the strongly coupled regime. Observation of such an effect would therefore rely on the detection of the scalar radiation that is produced during scalarisation. This work provides a basis on which further studies can be undertaken using codes that employ a moving-punctures approach to managing singularities in the numerical domain. It is therefore an important step forward in our ability to analyse modifications of general relativity in gravitational wave observations.