Late-Time Evolution of Realistic Rotating Collapse and The No-Hair Theorem

TL;DR

This paper analytically investigates the late-time behavior of perturbations around rotating black holes, confirming the no-hair theorem by demonstrating inverse power-law tails in various asymptotic regions and analyzing their dependence on field spin.

Contribution

It provides a detailed analytical study of late-time tails of perturbations in Kerr spacetimes, highlighting spin-dependent damping exponents and the effects of frame dragging on multipole coupling.

Findings

Inverse power-law tails develop at all asymptotic regions.

Damping exponents at timelike infinity and horizon are spin-independent.

Damping exponents at null infinity depend on the field's spin.

Abstract

We study analytically the asymptotic late-time evolution of realistic rotating collapse. This is done by considering the asymptotic late-time solutions of Teukolsky's master equation, which governs the evolution of gravitational, electromagnetic, neutrino and scalar perturbations fields on Kerr spacetimes. In accordance with the no-hair conjecture for rotating black-holes we show that the asymptotic solutions develop inverse power-law tails at the asymptotic regions of timelike infinity, null infinity and along the black-hole outer horizon (where the power-law behaviour is multiplied by an oscillatory term caused by the dragging of reference frames). The damping exponents characterizing the asymptotic solutions at timelike infinity and along the black-hole outer horizon are independent of the spin parameter of the fields. However, the damping exponents at future null infinity are spin dependent. The late-time tails at all the three asymptotic regions are spatially dependent on the spin parameter of the field. The rotational dragging of reference frames, caused by the rotation of the black-hole (or star) leads to an active coupling of different multipoles.