On the universality of late-time ringdown tail

TL;DR

This paper analytically demonstrates the universality of late-time black hole tail decay in General Relativity, showing it depends on the asymptotic decay of the effective potential and is robust against environmental matter effects.

Contribution

It provides a rigorous proof of tail universality for potentials decaying as 1/r^2 and extends understanding to various black hole and perturbation types.

Findings

Tail decay is universal for potentials decaying as 1/r^2.

Decay rate varies with potential decay as 1/r^α for 1<α<2.

Tails are insensitive to matter distributions like dark matter halos.

Abstract

The late time response of vacuum black holes in General Relativity is notoriously governed by power law tails arising from the wave scattering off the curved spacetime geometry far from the black hole. While it is known that such tails are universal to a certain extent, a precise characterization of their key ingredients is missing. Here we provide an analytical proof that the tail fall-off is universal for any effective potential asymptotically decaying as $1/r^2$, while the power law decay is different if the potential decays as $1/r^\alpha$ with $1<\alpha<2$. This result extends and revises some previous work and is in agreement with numerical analyses. Our proof is based on an analytical evaluation of the branch cut contribution to the Green function, and includes charged black holes, different kinds of perturbations, Teukolsky equation for the Kerr metric, exotic compact objects, extensions of General Relativity, and environmental effects. In the latter case, our results indicate that tails are largely insensitive to a wide range of physically motivated matter distributions around black holes, including the Navarro Frenk White profile commonly used to model dark matter.