Are scalar-Gauss-Bonnet and higher-curvature theories well-posed in black hole mergers?
In plain words
To simulate merging black holes in a modified theory, its equations must give a unique, stable evolution from given starting data. Some popular theories lose this property when gravity becomes strong.
Precise statement
For Einstein-scalar-Gauss-Bonnet gravity, L = R/(16 pi G) - (1/2)(grad phi)^2 + alpha f(phi) $G_{\mathrm{GB}}$ with G_GB the Gauss-Bonnet invariant, and for general Horndeski theories, strong hyperbolicity holds in modified harmonic gauge at weak coupling (Kovacs and Reall 2020). Determine the maximal coupling $\alpha/M^2$ for which binary black hole evolutions stay strongly hyperbolic through merger, and whether effective-field-theory fixing of the equations converges to a unique answer as the fixing is removed. An answer is a theorem or convergent numerical evidence with the coupling threshold.
What would settle it
Convergent merger simulations mapping the loss of hyperbolicity versus coupling, backed by a theorem on the fixing procedure.
Status in the literature
Well-posedness at weak coupling is proved (2020); simulations show loss of hyperbolicity at larger couplings, with theory-dependent thresholds.