Black hole dynamics in Effective Field Theory extensions to General Relativity

Abstract

This thesis aims to develop and implement mathematical and numerical techniques to enable the study of deviations from General Relativity (GR) in the nonlinear regime. The focus is on studying the nonlinear dynamics of higher derivative Effective Field Theory (EFT) extensions to GR and employing innovative methods to address the associated mathematical and practical challenges. To this end, we utilize two crucial techniques: the Fixing the Equations method, which controls spurious high frequencies, and the Order reduction approach to address challenges related to higher than second order time derivatives and ghosts.

The research starts with a detailed study of black hole dynamics in a higher derivative extension of General Relativity described by a dimension-eight operator EFT. A fully nonlinear/non-perturbative treatment is presented for constructing initial data and studying its dynamical behavior in spherical symmetry when coupled to a massless scalar field.

Subsequently, we extend the previous work to explore the evolution of black holes merging in quasi-circular orbits within the same higher-derivative EFT extension. This scenario poses more demanding challenges; a toy model and the single-boosted black hole scenario are considered to build up to the binary merger case. The effects of modifications on the dynamics and gravitational wave emission in the binary merger scenario are studied.

The research work culminates with a study of gravitational collapse in Quadratic Gravity, the leading order correction to GR from an EFT perspective in the presence of matter fields. An Order Reduction approach is used to eliminate additional degrees of freedom associated with higher order time derivatives. We study the collapse of a massless scalar field into a black hole in spherical symmetry. We explore the stability of our simulations, whether the solutions remain within the bounds of EFT, and their deviations from General Relativity during the collapse.