Binary Black Holes in Modified Gravity

TL;DR

This thesis uses numerical relativity to study gravitational waves from binary black holes in modified gravity theories, revealing significant waveform differences from GR and developing new computational tools.

Contribution

It provides the first detailed numerical analysis of binary black hole mergers in cubic Horndeski theories and introduces a versatile apparent horizon finder for numerical relativity.

Findings

Waveform mismatch exceeds 30% in some regimes

Waveform shifts are larger than expected from small parameters

Developed a new tool for horizon finding in numerical relativity

Abstract

In this thesis, we use numerical relativity to investigate gravitational waves from binary black holes in extensions of GR. We first study spherically symmetric gravitational collapse in cubic Horndeski theories of gravity. By varying the coupling constants and the initial amplitude of the scalar field, we determine the region in the space of couplings and amplitudes for which it is possible to construct global solutions to the Horndeski theories. Furthermore, we identify the regime of validity of effective field theory (EFT) as the sub-region for which a certain weak coupling condition remains small at all times. We study black hole binary mergers in these cubic Horndeski theories of gravity, treating them fully non-linearly. In the regime of validity of EFT, the mismatch of the gravitational wave strain between Horndeski and GR (coupled to a scalar field) can be larger than $30\%$ in the Advanced LIGO mass range. Initial data and coupling constants are chosen so the theory always remains in the weakly coupled regime. We observe that the waveform in Horndeski theories is shifted by an amount much larger than the smallness parameter that controls initial data. This effect is generic and may be present in other theories of gravity involving higher derivatives. We explore a higher-order curvature correction of GR. Guided by toy models, we develop systems capable of reproducing the low energy behaviour of many such theories with a fully nonlinear/non-perturbative approach. We evolve binary black holes, observing a shift in phase accumulated over time which is not statistically significant when compared to GR, for the methods and coupling used. Finally, we present AHFinder, a flexible multi-purpose tool to find apparent horizons in the open-source numerical relativity code GRChombo.