# Scalar Fields in Numerical General Relativity

## TL;DR

This paper introduces GRChombo, a new Numerical Relativity code with adaptive mesh refinement, enabling detailed simulations of complex spacetime phenomena like black hole mergers and scalar field collapse.

## Contribution

The paper presents the development and validation of GRChombo, a novel NR code that incorporates full AMR and parallelism, allowing for advanced studies of inhomogeneous scalar fields in GR.

## Key findings

- GRChombo can stably evolve black hole mergers.
- It enables exploration of inhomogeneous initial conditions.
- It reveals critical behavior in scalar field collapse.

## Abstract

Einstein's field equation of General Relativity (GR) has been known for over 100 years, yet it remains challenging to solve analytically in strongly relativistic regimes, particularly where there is a lack of a priori symmetry. Numerical Relativity (NR) - the evolution of the Einstein Equations using a computer - is now a relatively mature tool which enables such cases to be explored. In this thesis, a description is given of the development and application of a new Numerical Relativity code, GRChombo. GRChombo uses the standard BSSN formalism, incorporating full adaptive mesh refinement (AMR) and massive parallelism via the Message Passing Interface (MPI). The AMR capability permits the study of physics which has previously been computationally infeasible in a full 3+1 setting. The functionality of the code is described, its performance characteristics are demonstrated, and it is shown that it can stably and accurately evolve standard spacetimes such as black hole mergers. We use GRChombo to study the effects of inhomogeneous initial conditions on the robustness of small and large field inflationary models. and investigate the critical behaviour which occurs in the collapse of both spherically symmetric and asymmetric scalar field bubbles.