Nonlinearities of Schwarzschild Black Hole Head-on Collisions

TL;DR

This paper analytically derives the amplitude of quadratic quasi-normal modes generated during the ringdown phase of gravitational waves from ultra-relativistic head-on collisions of non-spinning Schwarzschild black holes, highlighting the effectiveness of second-order perturbation theory.

Contribution

It introduces a simple bootstrapping method within second-order perturbation theory to analytically compute nonlinear effects in black hole collisions.

Findings

Quadratic quasi-normal mode amplitudes are derived analytically.

Second-order perturbation theory effectively models nonlinearities in black hole collisions.

Nonlinear effects can be captured with a straightforward analytical approach.

Abstract

We derive analytically the amplitude of the quadratic quasi-normal mode generated in the ringdown stage of the gravitational waveform produced by the ultra-relativistic head-on collision of two non-spinning Schwarzschild black holes. Although being a highly nonlinear event, second-order perturbation theory suffices and that nonlinearities may be derived by a simple bootstrapping procedure.