Price's law from quasinormal modes

TL;DR

This paper demonstrates that Price's law tail for Schwarzschild perturbations can be derived from the sum of Schwarzschild-de Sitter quasinormal modes as the cosmological constant approaches zero.

Contribution

It introduces a novel approach to derive Price's law tail using quasinormal modes in the Schwarzschild-de Sitter spacetime in the limit of vanishing cosmological constant.

Findings

Price's tail can be obtained from quasinormal modes

The method connects Schwarzschild and Schwarzschild-de Sitter spacetimes

Provides insight into perturbation decay behavior

Abstract

We show that Price's power-law tail for perturbations of Schwarzschild, $t^{-2\ell-3}$ as $t\to \infty$, can be obtained from a sum of Schwarzschild-de Sitter quasinormal modes in the limit $\Lambda \to 0^+$.