Slowly decaying tails of massive scalar fields in spherically symmetric spacetimes

TL;DR

This paper investigates the late-time decay behavior of massive scalar fields in spherically symmetric spacetimes, revealing conditions under which long-lived oscillating tails occur, especially in black hole environments.

Contribution

It extends previous findings by analyzing the conditions for slow decay tails in various spherically symmetric spacetimes, including black holes and stars.

Findings

Long-lived oscillating tails decay as t^{-5/6} at late times.

Such tails are typically observed at timelike infinity in black hole spacetimes.

The tails may not persist around normal stars due to different scattering effects.

Abstract

We study the dominant late-time behaviors of massive scalar fields in static and spherically symmetric spacetimes. Considering the field evolution in the far zone where the gravitational field is weak, we show under which conditions the massive field oscillates with an amplitude that decays slowly as $t^{-5/6}$ at very late times, as previously found in (say) the Schwarzschild case. Our conclusion is that this long-lived oscillating tail is generally observed at timelike infinity in black hole spacetimes, while it may not be able to survive if the central object is a normal star. We also discuss that such a remarkable backscattering effect is absent for the field near the null cone at larger spatial distances.