Dynamics of Scalar Fields in the Background of Rotating Black Holes

TL;DR

This paper numerically investigates how massless scalar fields evolve around rotating black holes, revealing that late-time behavior is similar to non-rotating cases regardless of black hole spin.

Contribution

It provides a detailed numerical analysis of scalar field dynamics in rotating black hole backgrounds, including both slow and rapid rotation regimes.

Findings

Late-time scalar field decay follows power-law behavior similar to Schwarzschild black holes.

Rotation does not significantly alter the asymptotic decay rate of scalar fields.

The study extends understanding of scalar field evolution to rotating black hole spacetimes.

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 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.