Late time decay of scalar, electromagnetic, and gravitational perturbations outside rotating black holes

TL;DR

This paper analytically investigates the late-time decay of scalar, electromagnetic, and gravitational perturbations outside rotating Kerr black holes, revealing mode-dependent power-law decay rates and mode dominance behaviors.

Contribution

It provides the first detailed analytic derivation of late-time decay rates for various fields around Kerr black holes, including mode-specific indices and exact r-dependence expressions.

Findings

Decay rates depend on mode and spin, with dominant modes dying off as t^{-2|s|-3}.

Some modes decay slower than in Schwarzschild backgrounds.

Non-axially symmetric modes dominate late-time behavior along the event horizon.

Abstract

We study analytically, via the Newman-Penrose formalism, the late time decay of scalar, electromagnetic, and gravitational perturbations outside a realistic rotating (Kerr) black hole. We find a power-law decay at timelike infinity, as well as at null infinity and along the event horizon (EH). For generic initial data we derive the power-law indices for all radiating modes of the various fields. We also give an exact analytic expression (accurate to leading order in 1/t) for the r-dependence of the late time tail at any r. Some of our main conclusions are: (i) For generic initial data, the late time behavior of the fields is dominated by the mode l=|s| (with s being the spin parameter), which dies off at fixed $r$ as $t^{-2|s|-3}$ --- as in the Schwarzschild background. (ii) However, other modes admit decay rates slower than in the Schwarzschild case. (iii) For s>0 fields, non-axially symmetric modes dominate the late time behavior along the EH. These modes oscillate along the null generators of the EH.