Quasinormal modes, echoes and the causal structure of the Green's function

Understand

Quasinormal modes describe the return to equilibrium of a perturbed system, in particular the ringdown phase of a black hole merger.

• But as globally-defined quantities, the quasinormal spectrum can be highly sensitive to global structure, including distant small perturbations to the potential.
• In what sense are quasinormal modes a property of the resulting black hole? We explore this question for the linearized perturbation equation with two potentials having disjoint bounded support.
• We give a composition law for the Wronskian that determines the quasinormal frequencies of the combined system.