Wiggly tails: a gravitational wave signature of massive fields around black holes

TL;DR

This paper investigates how massive fields around black holes influence gravitational wave signals, revealing distinctive late-time wiggles and patterns that could indicate the presence of such fields, using linear perturbation analysis.

Contribution

It demonstrates that linear gravitational perturbation analysis captures the characteristic wiggles in gravitational wave tails caused by massive fields around black holes, confirming features seen in non-linear studies.

Findings

Late-time tails contain small amplitude wiggles at the quasi-bound state frequency.

Wiggles and beating patterns are present at the linear level, not just non-linear.

The tail's power law becomes universal far from the black hole.

Abstract

Massive fields can exist in long-lived configurations around black holes. We examine how the gravitational wave signal of a perturbed black hole is affected by such `dirtiness' within linear theory. As a concrete example, we consider the gravitational radiation emitted by the infall of a massive scalar field into a Schwarzschild black hole. Whereas part of the scalar field is absorbed/scattered by the black hole and triggers gravitational wave emission, another part lingers in long-lived quasi-bound states. Solving numerically the Teukolsky master equation for gravitational perturbations coupled to the massive Klein-Gordon equation, we find a characteristic gravitational wave signal, composed by a quasi-normal ringing followed by a late time tail. In contrast to `clean' black holes, however, the late time tail contains small amplitude wiggles with the frequency of the dominating quasi-bound state. Additionally, an observer dependent beating pattern may also be seen. These features were already observed in fully non-linear studies; our analysis shows they are present at linear level, and, since it reduces to a 1+1 dimensional numerical problem, allows for cleaner numerical data. Moreover, we discuss the power law of the tail and that it only becomes universal sufficiently far away from the `dirty' black hole. The wiggly tails, by constrast, are a generic feature that may be used as a smoking gun for the presence of massive fields around black holes, either as a linear cloud or as fully non-linear hair.