We present a numerical study of the time evolution of perturbations of rotating black holes. The solutions are obtained by integrating the Teukolsky equation written as a first-order in time, coupled system of equations, in a form that explicitly captures its hyperbolic structure. We address the numerical difficulties of solving the equation in its original form. We follow the propagation of generic initial data through the burst, quasinormal ringing and power-law tail phases. In particular, we calculate the effects due to the rotation of the black hole on the scattering of incident gravitational wave pulses. These results may help explain how the angular momentum of the black hole affects the gravitational waves that are generated during the final stages of black hole coalescence.

We study the evolution of massless scalar waves propagating on spherically symmetric spacetimes with a nonzero cosmological constant. Considering test fields on both Schwarzschild-de Sitter and Reissner-Nordström-de Sitter backgrounds, we demonstrate the existence of exponentially decaying tails at late times. Interestingly the ℓ = 0 mode asymptotes to a non-zero value, contrasting the asymptotically flat situation. We also compare these results, for ℓ = 0, with a numerical integration of the Einstein-scalar field equations, finding good agreement between the two. Finally, the significance of these results to the study of the Cauchy horizon stability in black hole-de Sitter spacetimes is discussed.

A numerical study of the evolution of a massless scalar field in the background of rotating black holes is presented. First, solutions to the wave equation are obtained for slowly rotating black holes. In this approximation, the background geometry is treated as a perturbed Schwarzschild spacetime with the angular momentum per unit mass playing the role of a perturbative parameter. To first order in the angular momentum of the black hole, the scalar wave equation yields two coupled one-dimensional evolution equations for a function representing the scalar field in the Schwarzschild background and a second field that accounts for the rotation. Solutions to the wave equation are also obtained for rapidly rotating black holes. In this case, the wave equation does not admit complete separation of variables and yields a two-dimensional evolution equation. The study shows that, for rotating black holes, the late time dynamics of a massless scalar field exhibit the same power-law behavior as in the case of a Schwarzschild background independently of the angular momentum of the black hole.