Dynamics of scalar fields in the background of rotating black holes

Abstract

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. In this approximation, the late time dynamics of a massless scalar field exhibit the same power-law behavior as in the case of a Schwarzschild background. Solutions to the wave equation are also obtained for rapidly rotating black holes. In this case, owing to higher order terms in the angular momentum, the wave equation does not admit complete separation of variables and yields a two-dimensional evolution equation. The study shows that, depending on initial conditions, the late-time dynamics of a massless scalar field is dominated by the lowest-allowed mode with respect to $l$ for a fixed value of $m$.