We derive the Teukolsky equation for perturbations of a Kerr spacetime when the spacetime metric is written in either ingoing or outgoing Kerr-Schild form. We also write explicit formulae for setting up the initial data for the Teukolsky equation in the time domain in terms of a 3-metric and an extrinsic curvature. The motivation of this work is to have in place a formalism to study the evolution in the 'close limit' of two recently proposed solutions to the initial-value problem in general relativity that are based on Kerr-Schild slicings. A perturbative formalism in horizon-penetrating coordinates is also very desirable in connection with numerical relativity simulations using black hole 'excision'.
Publication Source (Journal or Book title)
Classical and Quantum Gravity
Campanelli, M., Khanna, G., Laguna, P., Pullin, J., & Ryan, M. (2001). Perturbations of the Kerr spacetime in horizon-penetrating coordinates. Classical and Quantum Gravity, 18 (8), 1543-1554. https://doi.org/10.1088/0264-9381/18/8/310