Conformal Scattering and the Goursat Problem for Dirac Fields in the Interior of Charged Spherically Symmetric Black Holes

Abstract

We construct a conformal scattering theory for Dirac fields in the interior of a Reissner-Nordström-like black hole, between the black hole event horizon and the Cauchy horizon. The main result is a resolution of the characteristic Cauchy problem for the Dirac equation on the horizons by solving a system of wave equations and re-interpreting its solution as the components of the required Dirac solution.

arXiv comment13 pages, 2 figures

References in corpus (5)

• A scattering theory for linear waves on the interior of Reissner-Nordström black holes
• Conformal Scattering of Maxwell Fields on Reissner-Nordstrøm-de Sitter Black Hole Spacetimes
• Reissner-Nordstrøm-de Sitter Manifold : Photon Sphere and Maximal Analytic Extension
• Scattering theory for Dirac fields inside a Reissner-Nordström-type black hole
• Decay of Maxwell Fields on Reissner-Nordstrøm-de Sitter Black Holes

Cited by in corpus (6)

• Strong Cosmic Censorship in the presence of matter: the decisive effect of horizon oscillations on the black hole interior geometry
• Conformal scattering theory for the Dirac field on Kerr spacetime
• On the Scattering of Waves inside Charged Spherically Symmetric Black Holes
• Cauchy and Goursat problems for the generalized spin zero rest-mass fields on Minkowski spacetime
• Conformal Scattering of Maxwell Potentials
• Conformal scattering theories for tensorial wave equations on Schwarzschild spacetime