Asymptotic tails of massive scalar fields in Schwarzschild background

TL;DR

This paper analyzes the late-time decay behavior of massive scalar fields in Schwarzschild spacetime, revealing a specific power-law decay and oscillation pattern influenced by spacetime curvature.

Contribution

It demonstrates the decay rate and oscillation characteristics of scalar fields in Schwarzschild background, extending understanding of tail behavior in curved spacetime.

Findings

Scalar field tails decay as t^{-5/6} at late times

Oscillations have a period of 2π/m, modulated by phase shifts

Behavior similar to that in nearly extreme Reissner-Nordström spacetime

Abstract

We investigate the asymptotic tail behavior of massive scalar fields in Schwarzschild background. It is shown that the oscillatory tail of the scalar field has the decay rate of $t^{-5/6}$ at asymptotically late times, and the oscillation with the period $2\pi/m$ for the field mass $m$ is modulated by the long-term phase shift. These behaviors are qualitatively similar to those found in nearly extreme Reissner-Nordstr\"{o}m background, which are discussed in terms of a resonant backscattering due to the space-time curvature.