Decay of Solutions of the Teukolsky Equation for Higher Spin in the Schwarzschild Geometry

TL;DR

This paper proves the linear stability of Schwarzschild black holes under electromagnetic and gravitational perturbations by demonstrating decay of solutions to the Teukolsky equation for higher spins, specifically for electromagnetic and gravitational cases.

Contribution

It establishes decay and stability results for solutions of the Teukolsky equation with higher spins in Schwarzschild geometry, extending previous stability analyses.

Findings

Solutions decay in local $L^ty$ norm

Schwarzschild black hole is linearly stable under perturbations

Decay holds for smooth, compactly supported initial data

Abstract

We prove that the Schwarzschild black hole is linearly stable under electromagnetic and gravitational perturbations. Our method is to show that for spin $s=1$ or $s=2$, solutions of the Teukolsky equation with smooth, compactly supported initial data outside the event horizon, decay in $L^\infty_{loc}$.