An Electrodynamic Perspective of Black Holes

Numerical relativity (NR) is a powerful modeling tool for the dynamics of general-relativistic systems that are difficult to analyze analytically. Prior work has led to a tetrad formulation of the 3+1 decomposition of the Einstein field equations (EFE) that bears a striking resemblance to electrodynamics, done by recasting Einstein’s equations into a set of coupled nonlinear Maxwell equations. We use gravitational electric and magnetic fields developed from this theory to analytically probe Schwarzschild and Kerr solutions to the EFE. We compare the resulting Kerr dynamics with a numerical simulation of the Kerr spacetime. We then extend this analysis to visualize the inspiral, merger, and ring-down of a binary black hole collision simulated in moving puncture gauge.