Second Order Perturbations of Kerr Black Holes: Reconstruction of the Metric

Understand

Motivated by gravitational wave observations of binary black hole mergers, we present a procedure to compute the leading order nonlinear gravitational wave interactions around a Kerr black hole.

• We describe the formalism used to derive the equations for second order perturbations.
• We develop a procedure that allows us to reconstruct the first order metric perturbation solely from knowledge of the solution to the first order Teukolsky equation, without the need of Hertz potentials.
• Finally, we illustrate this metric reconstruction procedure in the asymptotic limit for the first order quasi-normal modes of Kerr.