The wave equation on the Schwarzschild metric II: Local decay for the spin 2 Regge Wheeler equation

TL;DR

This paper proves that solutions to the spin 2 Regge-Wheeler equation on the Schwarzschild metric exhibit local decay, with weighted norms remaining square-integrable over time and space, using commutator techniques.

Contribution

It establishes uniform local decay estimates for all relevant spherical harmonics of the spin 2 perturbations, extending previous results to a broader class of solutions.

Findings

Weighted norms of solutions are in L^2 of time and space.

Decay estimates apply uniformly across all relevant spherical harmonics.

Uses commutator methods to achieve results.

Abstract

Odd-type spin 2 perturbations of Einstein's equation can be reduced to the scalar Regge-Wheeler equation. We show that the weighted norms of solutions are in L^2 of time and space. This result uses commutator methods and applies uniformly to all relevant spherical harmonics.