Decay Rates for Spherical Scalar Waves in the Schwarzschild Geometry

TL;DR

This paper derives the exact decay rate for spherical scalar waves in Schwarzschild spacetime using spectral methods, providing precise long-term behavior of solutions with specific initial data.

Contribution

It introduces a spectral integral approach to determine the precise decay rates of scalar waves in Schwarzschild geometry, advancing understanding of wave behavior in curved spacetime.

Findings

Exact decay rate for spherical scalar waves derived

Spectral integral representation used for analysis

Results applicable to smooth, compactly supported initial data

Abstract

The Cauchy problem is considered for the scalar wave equation in the Schwarzschild geometry. Using an integral spectral representation we derive the exact decay rate for solutions of the Cauchy problem with spherical symmetric initial data, which is smooth and compactly supported outside the event horizon.