Generation and propagation of nonlinear quasi-normal modes of a Schwarzschild black hole

Understand

In the analysis of a binary black hole coalescence, it is necessary to include gravitational self-interactions in order to describe the transition of the gravitational wave signal from the merger to the ringdown stage.

• In this paper we study the phenomenology of the generation and propagation of nonlinearities in the ringdown of a Schwarzschild black hole, using second-order perturbation theory.
• Following earlier work, we show that the Green's function and its causal structure determines how both first-order and second-order perturbations are generated, and hence highlight that both of these solutions share some physical properties.
• In particular, we discuss the sense in which both linear and quadratic quasi-normal modes (QNMs) are generated in the vicinity of the peak of the gravitational potential barrier (loosely referred to as the light ring).