The Cauchy Problem for the Wave Equation in the Schwarzschild Geometry
Johann Kronthaler
TL;DR
This paper studies the scalar wave equation in Schwarzschild spacetime, deriving an integral spectral representation of solutions and proving they decay over time, enhancing understanding of wave behavior in black hole backgrounds.
Contribution
It introduces a new integral spectral representation for solutions to the wave equation in Schwarzschild geometry and establishes their pointwise decay over time.
Findings
Derived an integral spectral representation for solutions.
Proved pointwise decay of solutions in time.
Enhanced understanding of wave dynamics in black hole spacetimes.
Abstract
The Cauchy problem is considered for the scalar wave equation in the Schwarzschild geometry. We derive an integral spectral representation for the solution and prove pointwise decay in time.
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