Quasi-spherical approximation for rotating black holes

TL;DR

This paper introduces a numerical quasi-spherical approximation method for calculating gravitational waveforms from coalescing black holes, validated against Kerr black holes with high angular momentum, showing promising accuracy and low spurious radiation.

Contribution

It presents a novel numerical scheme for gravitational waveform computation that effectively handles rotating black holes with high angular momentum.

Findings

Strain is monotonic, not wavelike.

Spurious gravitational energy is below 1%.

Method remains accurate for angular momentum up to 70%.

Abstract

We numerically implement a quasi-spherical approximation scheme for computing gravitational waveforms for coalescing black holes, testing it against angular momentum by applying it to Kerr black holes. As error measures, we take the conformal strain and specific energy due to spurious gravitational radiation. The strain is found to be monotonic rather than wavelike. The specific energy is found to be at least an order of magnitude smaller than the 1% level expected from typical black-hole collisions, for angular momentum up to at least 70% of the maximum, for an initial surface as close as $r=3m$.