Can Oscillatory and Persistent Nonlinearities Be Bridged in Black Hole Ringdown?

TL;DR

This paper explores the relationship between quadratic quasinormal modes and the Christodoulou memory effect in black hole ringdown, proposing a bridge mediated by parameters of the remnant black hole, with implications for gravitational wave detection.

Contribution

It introduces a novel connection between nonlinear phenomena in black hole physics, offering a new method to test gravity through gravitational wave observations.

Findings

Bridge coefficients depend on remnant black hole parameters.

Future detectors can probe the relation between QQNMs and memory effect.

Provides a new perspective on nonlinear regimes in general relativity.

Abstract

Quadratic quasinormal modes (QQNMs) and Christodoulou memory effect are key nonlinear phenomena in gravitational wave physics. QQNMs characterize the near zone nonlinear response of a perturbed black hole, whereas the memory effect is a nonlinear remnant imprinted at null infinity by outgoing radiation. This naturally raises the question of whether and in what sense the two can be bridged. We show that they are related through bridge coefficients which depend primarily on remnant black hole parameters during ringdown. Future space-based gravitational wave detectors can probe this relation. These results provide a new avenue for testing gravity and a fresh perspective on the nonlinear regime of general relativity.