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We study the even-parity ℓ = 2 perturbations of a Schwarzschild black hole to second order. The Einstein equations can be reduced to a single linear wave equation with a potential and a source term. The source term is quadratic in terms of the first-order perturbations. This provides a formalism to address the validity of many first-order calculations of interest in astrophysics. © 1996 IOP Publishing Ltd.

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Classical and Quantum Gravity