Spin dependence of black hole ringdown nonlinearities

TL;DR

This paper investigates the nonlinear effects in black hole ringdown signals using second-order perturbation theory, revealing how black hole spin influences the excitation of nonlinear modes and cautioning against extrapolations to high spins.

Contribution

It provides a detailed analysis of second-order mode excitation in black hole ringdowns, highlighting the dependence on spin and initial data, which was previously less understood.

Findings

Second-order mode amplitudes are mildly affected by initial data.

Higher black hole spins significantly suppress second-order mode excitation.

Results suggest caution when applying Kerr-CFT extrapolations to subextremal spins.

Abstract

The nonlinear character of general relativity leaves its imprint in the coalescence of two black holes, from the inspiral to the final ringdown stage. To quantify the impact of nonlinearities, we work at second order in black hole perturbation theory and we study the excitation of second-order modes relative to the first-order modes that drive them as we vary the black hole spin and the initial data for the perturbations. The relative amplitude of second-order modes is only mildly dependent on the initial data that we consider, but it strongly decreases for large black hole spins. This implies that the extrapolation of calculations based on the Kerr-CFT correspondence to subextremal Kerr black holes should be viewed with caution.