Revisiting Event Horizon Finders

TL;DR

This paper compares three methods for locating event horizons in numerical black hole simulations, finding that backward geodesic integration is most robust and revealing detailed horizon dynamics during mergers.

Contribution

It implements and evaluates three event horizon finding techniques, demonstrating the robustness of backward geodesic integration and analyzing horizon behavior during black hole mergers.

Findings

Backward geodesic integration is most robust for horizon finding.

The exponential approach rate of null surfaces matches black hole surface gravity.

The apparent horizon closely approximates the event horizon at all times.

Abstract

Event horizons are the defining physical features of black hole spacetimes, and are of considerable interest in studying black hole dynamics. Here, we reconsider three techniques to localise event horizons in numerical spacetimes: integrating geodesics, integrating a surface, and integrating a level-set of surfaces over a volume. We implement the first two techniques and find that straightforward integration of geodesics backward in time to be most robust. We find that the exponential rate of approach of a null surface towards the event horizon of a spinning black hole equals the surface gravity of the black hole. In head-on mergers we are able to track quasi-normal ringing of the merged black hole through seven oscillations, covering a dynamic range of about 10^5. Both at late times (when the final black hole has settled down) and at early times (before the merger), the apparent horizon is found to be an excellent approximation of the event horizon. In the head-on binary black hole merger, only {\em some} of the future null generators of the horizon are found to start from past null infinity; the others approach the event horizons of the individual black holes at times far before merger.