Algebraic Classification of Numerical Spacetimes and Black-Hole-Binary Remnants

TL;DR

This paper introduces a method to classify the algebraic type of numerical black-hole spacetimes using Newman-Penrose scalars, revealing how such spacetimes evolve post-merger and testing the no-hair theorem.

Contribution

The paper develops a novel technique for algebraic classification of numerical spacetimes from black-hole mergers using Weyl scalars, enabling new insights into spacetime properties.

Findings

Post-merger, spacetime quickly approaches Petrov type II.

Spacetime approaches Petrov type D over longer timescales.

Technique facilitates exploration of the no-hair theorem in dynamic mergers.

Abstract

In this paper we develop a technique for determining the algebraic classification of a numerical spacetime, possibly resulting from a generic black-hole-binary merger, using the Newman-Penrose Weyl scalars. We demonstrate these techniques for a test case involving a close binary with arbitrarily oriented spins and unequal masses. We find that, post merger, the spacetime quickly approaches Petrov type II, and only approaches type D on much longer timescales. These techniques allow us to begin to explore the validity of the "no-hair theorem" for generic merging-black-hole spacetimes.