Numerical constructions of novel static solutions to the Einstein Field Equations

The Einstein field equations (EFE) are notoriously difficult to solve due to their high degree of nonlinearity. To better understand the nature of gravity and other nonlinear phenomena, we must develop tools that can effectively address this nonlinearity. This project investigates numerical constructions of novel static solutions to the EFE. In particular, we employ spectral methods with an iterative scheme to address the nonlinearity of the EFE and solve the system for a static solution. This method provides an efficient means of converging to a solution for nonlinear systems with a high degree of accuracy. We discuss the physical interpretations of these solutions and the limitations of the numerical techniques employed. We aim to demonstrate the usefulness of these numerical methods and to build a framework for understanding more complex spacetimes and other nonlinear systems.