Late time tails from momentarily stationary, compact initial data in Schwarzschild spacetimes

TL;DR

This paper investigates the late-time decay behavior of perturbations in Schwarzschild spacetime, revealing that momentarily static, compact initial data lead to a different decay rate than previously known, due to unique properties of the Laplace transform.

Contribution

It explains why momentarily static initial data produce a different decay rate by analyzing Laplace transforms and time-domain features, highlighting a special case in black hole perturbation theory.

Findings

Momentarily static initial data cause a decay rate of t^{-2L-4}.

Laplace transform analysis reveals the exceptional nature of this case.

Time-domain description clarifies the unique features of the decay process.

Abstract

An L-pole perturbation in Schwarzschild spacetime generally falls off at late times t as t^{-2L-3}. It has recently been pointed out by Karkowski, Swierczynski and Malec, that for initial data that is of compact support, and is initially momentarily static, the late-time behavior is different, going as t^{-2L-4}. By considering the Laplace transforms of the fields, we show here why the momentarily stationary case is exceptional. We also explain, using a time-domain description, the special features of the time development in this exceptional case.