Puncture Gauge Formulation for Einstein-Gauss-Bonnet Gravity and Four-Derivative Scalar-Tensor Theories in D+1 Spacetime Dimensions

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 scalarization" induced by the spin of the remnant black hole after the merger. As in previous studies using alternative gauges, we find that the scalarization occurs too late after the merger to impact 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 scalarization. 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 analyze modifications of general relativity in gravitational wave observations.