A Study of the Geometric Horizon Conjecture as Applied to a Binary Black Hole Merger

Abstract

We study the algebraic structure of the Weyl tensor by tracing the level--0 set of the complex scalar polynomial invariant, D, through a numerical simulation of a quasi-circular binary black hole merger. We approximate the level-0 sets of D with level--epsilon sets of |D| for small epsilon. We locate the local minima of |D| and find that the positions of these local minima correspond closely to the level-epsilon sets of |D| and we also compare with the level-0 sets of Re(D). The analysis provides strong evidence that the level-epsilon sets track a unique geometric horizon. By studying the behaviour of the zero sets of Re(D), Im(D) and their product, we observe that the level-epsilon set that best approximates this geometric horizon is given by epsilon = 0.001.