Nonlinear and Perturbative Evolution of Distorted Black Holes. II. Odd-parity Modes

TL;DR

This paper compares nonlinear and perturbative evolutions of nonrotating black holes with odd-parity distortions, demonstrating excellent agreement and advancing methods for studying more complex black hole systems.

Contribution

It introduces the second polarization mode in black hole perturbations and systematically compares nonlinear and linearized results using multiple techniques.

Findings

Excellent agreement between nonlinear and perturbative waveforms

Validation of perturbative methods for odd-parity black hole distortions

Progress towards studying rotating and more complex black hole systems

Abstract

We compare the fully nonlinear and perturbative evolution of nonrotating black holes with odd-parity distortions utilizing the perturbative results to interpret the nonlinear results. This introduction of the second polarization (odd-parity) mode of the system, and the systematic use of combined techniques brings us closer to the goal of studying more complicated systems like distorted, rotating black holes, such as those formed in the final inspiral stage of two black holes. The nonlinear evolutions are performed with the 3D parallel code for Numerical Relativity, {Cactus}, and an independent axisymmetric code, {Magor}. The linearized calculation is performed in two ways: (a) We treat the system as a metric perturbation on Schwarzschild, using the Regge-Wheeler equation to obtain the waveforms produced. (b) We treat the system as a curvature perturbation of a Kerr black hole (but here restricted to the case of vanishing rotation parameter a) and evolve it with the Teukolsky equation The comparisons of the waveforms obtained show an excellent agreement in all cases.