Abstract
We consider perturbations of a Schwarzschild black hole that can be of both even and odd parity, keeping terms up to second order in perturbation theory, for the l = 2 axisymmetric case. We develop explicit formulae for the evolution equations and radiated energies and waveforms using the Regge–Wheeler–Zerilli approach. This formulation is useful, for instance, for the treatment in the "close limit approximation" of the collision of counterrotating black holes.
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Nicasio, C.O., Gleiser, R. & Pullin, J. Second Order Perturbations of a Schwarzschild Black Hole: Inclusion of Odd Parity Perturbations. General Relativity and Gravitation 32, 2021–2042 (2000). https://doi.org/10.1023/A:1001994318436
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DOI: https://doi.org/10.1023/A:1001994318436