Conformal scattering and the Goursat problem for Dirac fields in the interior of charged spherically symmetric black holes

Mokdad Mokdad (1)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

In this paper, 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.

Mots clés: Conformal scattering theory; black hole interior; Reissner–Nordström metric; Goursat problem; dirac equation; Conformal Scattering theory; Black hole interior; Reissner-Nordström metric; Goursat Problem; Dirac equation; field theory: Dirac; black hole: charge; symmetry: rotation; scattering; conformal; horizon; Reissner-Nordstroem; boundary condition; resolution

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]; Physique mathématique [math-ph]

Mokdad Mokdad. Conformal scattering and the Goursat problem for Dirac fields in the interior of charged spherically symmetric black holes. Rev.Math.Phys., 2022, 34 (01), pp.2150037. ⟨10.1142/S0129055X21500379⟩. ⟨hal-03122306⟩