The Evolution of Distorted Rotating Black Holes I: Methods and Tests

TL;DR

This paper introduces a new numerical code for evolving distorted, rotating black holes, validating it through various tests, and exploring new phenomena in rotating black hole evolution and initial data configurations.

Contribution

The paper presents a novel numerical code for simulating rotating black holes, including new initial data sets and analysis of limiting slices, advancing computational methods in black hole physics.

Findings

Code accurately reproduces non-rotating black hole results

Successfully evolves Kerr spacetimes with known analytic properties

Identifies new features in rotating black hole evolution

Abstract

We have developed a new numerical code to study the evolution of distorted, rotating black holes. We discuss the numerical methods and gauge conditions we developed to evolve such spacetimes. The code has been put through a series of tests, and we report on (a) results of comparisons with codes designed to evolve non-rotating holes, (b) evolution of Kerr spacetimes for which analytic properties are known, and (c) the evolution of distorted rotating holes. The code accurately reproduces results of the previous NCSA non-rotating code and passes convergence tests. New features of the evolution of rotating black holes not seen in non-rotating holes are identified. With this code we can evolve rotating black holes up to about $t=100M$, depending on the resolution and angular momentum. We also describe a new family of black hole initial data sets which represent rotating holes with a wide range of distortion parameters, and distorted non-rotating black holes with odd-parity radiation. Finally, we study the limiting slices for a maximally sliced rotating black hole and find good agreement with theoretical predictions.