Tracking Black Holes in Numerical Relativity

TL;DR

This paper introduces a robust method for tracking black hole event horizons in numerical simulations using solutions of the hyperbolic eikonal equation, enabling detailed analysis of black hole mergers.

Contribution

It develops a novel level set viscosity solution approach to continuously monitor event horizon topology changes in complex black hole interactions.

Findings

Boundaries on the topology of merging black holes' throats

Estimated time of black hole merger

Quantitative analysis of black hole surface areas

Abstract

This work addresses and solves the problem of generically tracking black hole event horizons in computational simulation of black hole interactions. Solutions of the hyperbolic eikonal equation, solved on a curved spacetime manifold containing black hole sources, are employed in development of a robust tracking method capable of continuously monitoring arbitrary changes of topology in the event horizon, as well as arbitrary numbers of gravitational sources. The method makes use of continuous families of level set viscosity solutions of the eikonal equation with identification of the black hole event horizon obtained by the signature feature of discontinuity formation in the eikonal's solution. The method is employed in the analysis of the event horizon for the asymmetric merger in a binary black hole system. In this first such three dimensional analysis, we establish both qualitative and quantitative physics for the asymmetric collision; including: 1. Bounds on the topology of the throat connecting the holes following merger, 2. Time of merger, and 3. Continuous accounting for the surface of section areas of the black hole sources.