Universality of massive scalar field late-time tails in black-hole spacetimes

TL;DR

This study confirms that massive scalar fields exhibit a universal late-time tail decay in black-hole spacetimes, independent of black hole spin, mode, or initial data, extending previous Schwarzschild results to Kerr black holes.

Contribution

It demonstrates the universality of late-time tail behavior of massive scalar fields across different black-hole spacetimes, including Kerr black holes.

Findings

Late-time decay follows t^{-5/6} law with oscillations.

Decay rate is independent of black hole spin and mode.

Behavior is universal across initial data types.

Abstract

The late-time tails of a massive scalar field in the spacetime of black holes are studied numerically. Previous analytical results for a Schwarzschild black hole are confirmed: The late-time behavior of the field as recorded by a static observer is given by $\psi(t)\sim t^{-5/6}\sin [\omega (t)\times t]$, where $\omega(t)$ depends weakly on time. This result is carried over to the case of a Kerr black hole. In particular, it is found that the power-law index of -5/6 depends on neither the multipole mode $\ell$ nor on the spin rate of the black hole $a/M$. In all black hole spacetimes, massive scalar fields have the same late-time behavior irrespective of their initial data (i.e., angular distribution). Their late-time behavior is universal.