Complete null data for a black hole collision

TL;DR

This paper introduces an algorithm to compute complete event horizon data for binary black hole mergers, enabling detailed analysis of their geometry and the generation of gravitational waveforms.

Contribution

The paper presents a novel algorithm for calculating complete event horizon data, facilitating the study of binary black hole geometries and waveforms in both linear and nonlinear regimes.

Findings

Constructed a sequence of binary black hole horizons approaching a Schwarzschild horizon.

Provided global insights into the close limit for binary black holes.

Outlined the transition from perturbative to nonlinear regimes in black hole mergers.

Abstract

We present an algorithm for calculating the complete data on an event horizon which constitute the necessary input for characteristic evolution of the exterior spacetime. We apply this algorithm to study the intrinsic and extrinsic geometry of a binary black hole event horizon, constructing a sequence of binary black hole event horizons which approaches a single Schwarzschild black hole horizon as a limiting case. The linear perturbation of the Schwarzschild horizon provides global insight into the close limit for binary black holes, in which the individual holes have joined in the infinite past. In general there is a division of the horizon into interior and exterior regions, analogous to the division of the Schwarzschild horizon by the r=2M bifurcation sphere. In passing from the perturbative to the strongly nonlinear regime there is a transition in which the individual black holes persist in the exterior portion of the horizon. The algorithm is intended to provide the data sets for production of a catalog of nonlinear post-merger wave forms using the PITT null code.