Gauge-invariant perturbations of Schwarzschild black holes in horizon-penetrating coordinates - art. no. 084016

We derive a geometrical version of the Regge-Wheeler and Zerilli equations, which allows us to study gravitational perturbations on an arbitrary spher ically symmetric slicing of a Schwarzschild black hole. We explain how to o btain the gauge-invariant part of the metric perturbations from the amplitu des obeying our generalized Regge-Wheeler and Zerilli equations, and vice-v ersa. We also give a general expression for the radiated energy at infinity , and establish a relation between our geometrical equations and the Teukol sky formalism. The results presented in this paper are expected to be usefu l for the close-limit approximation to black hole collisions. for the Cauch y perturbative matching problem, and for the study of isolated horizons.