Scalar Field Collapse: Leveraging Numerical Relativity to Simulate Black Hole Formation and Localize Apparent Horizons

Abstract

This thesis explores models of collapsing matter by leveraging the dynamics of scalar fields. Understanding the evolution of these fields in curved spacetime, and the boundaries of any black holes that are formed in the process are interesting challenges in modern physics. The analysis of apparent horizons also provides valuable details about the nature of black holes, especially in evolving spacetimes where these horizons can change and interact. We provide a framework capable of creating comprehensive animations depicting the evolution of various scalar field configurations within a curved spacetime, and present a horizon finder tool, designed to accurately identify and display the location of any apparent horizons that emerge in our simulations. This project is intended to bring together advanced mathematics, theoretical physics, and cutting-edge numerical methods. We hope to further our understanding of scalar fields and black holes, while also providing powerful new tools to push the boundaries of visualization techniques in numerical relativity simulations.