The Cauchy Problem for the Wave Equation in the Schwarzschild Geometry

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.

33 pages

References in corpus (3)

• A proof of Price's law for the collapse of a self-gravitating scalar field
• An Integral Spectral Representation of the Propagator for the Wave Equation in the Kerr Geometry
• Scalar waves on a naked-singularity background

Cited by in corpus (5)

• Chaotic lensing around boson stars and Kerr black holes with scalar hair
• A proof of Price's Law on Schwarzschild black hole manifolds for all angular momenta
• Fundamental Solutions for the Klein-Gordon Equation in de Sitter Spacetime
• Asymptotic Behavior of Massless Dirac Waves in Schwarzschild geometry
• The Dirac equation across the horizons of the 5D Myers-Perry geometry : Separation of variables, radial asymptotic behaviour and Hamiltonian formalism