Nonlinearities in Kerr Black Hole Ringdown from the Penrose Limit

TL;DR

This paper presents an analytical method to compute nonlinear gravitational wave effects during Kerr black hole ringdown using the Penrose limit, revealing how these effects depend on black hole spin.

Contribution

It introduces a novel analytical approach to quantify nonlinearities in Kerr black hole ringdown through the Penrose limit, connecting quasi-normal modes to null geodesics.

Findings

Analytical expressions for amplitude and phase of quadratic quasi-normal modes.

Dependence of nonlinearities on black hole spin.

Connection between null geodesics and ringdown nonlinearities.

Abstract

We provide a fully analytical approach to calculate the nonlinearities of the gravitational waves in the ringdown of a Kerr black hole in the eikonal limit. The corresponding quasi-normal modes are associated to the orbits of a closed circular null geodesic and the problem can be analyzed by taking the Penrose limit around it. We calculate analytically the amplitude and the phase of the quadratic quasi-normal modes as well as its dependence on the black hole spin.