Fixing the dynamical evolution in scalar-Gauss-Bonnet gravity

One of the major obstacles to testing alternative theories of gravity with gravitational wave data from merging binaries of compact objects is the formulation of their field equations, which is often mathematically ill-suited for time evolutions. A possible way to address these delicate shortcomings is the fixing-the-equations approach, which was developed to control the behavior of the high-frequency modes of the solutions and the potentially significant flow towards ultra-violet modes. This is particularly worrisome in gravitational collapse, where even black hole formation might be insufficient to shield regions of the spacetime where these pathologies might arise. Here, we focus (as a representative example) on scalar-Gauss-Bonnet gravity, a theory which can lead to ill-posed dynamical evolutions, but with intriguing stationary black hole physics. We study the spherical collapse of a scalar pulse to a black hole in the fixing-the-equations approach, comparing the early stages of the evolution with the unfixed theory, and the later stages with its stationary limit. With this approach, we are able to evolve past problematic regions in the original theory, resolve black hole collapse and connect with the static black hole solutions. Our method can thus be regarded as providing a weak completion of the original theory, and the observed behavior lends support for considering previously found black hole solutions as a natural outcome of collapse scenarios.