Second-order perturbations of Kerr black holes: Formalism and reconstruction of the first-order metric

Nicholas Loutrel, Justin L. Ripley, Elena Giorgi, Frans Pretorius

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Abstract

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 quasinormal modes of Kerr. In a companion paper [J. L. Ripley et al., Phys. Rev. D 103, 104018 (2021)PRVDAQ2470-001010.1103/PhysRevD.103.104018] we present a numerical implementation of these ideas.

Original languageEnglish (US)
Article number104017
JournalPhysical Review D
Volume103
Issue number10
DOIs
StatePublished - May 18 2021

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy (miscellaneous)

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