Scattering theory for the Dirac equation on the Schwarzschild-Anti-de Sitter spacetime

Abstract

We show asymptotic completeness for linear massive Dirac fields on the Schwarzschild-Anti-de Sitter spacetime. The proof is based on a Mourre estimate. We also construct an asymptotic velocity for this field.

References in corpus (7)

• A scattering theory for the wave equation on Kerr black hole exteriors
• Microlocal analysis of asymptotically hyperbolic and Kerr-de Sitter spaces
• Boundedness and growth for the massive wave equation on asymptotically anti-de Sitter black holes
• A scattering theory construction of dynamical vacuum black holes
• Creation of fermions by rotating charged black-holes
• Asymptotic completeness for superradiant Klein-Gordon equations and applications to the De Sitter Kerr metric
• Semiclassical resonances for a two-level Schrödinger operator with a conical intersection

Cited by in corpus (4)

• Hadamard property of the in and out states for Klein-Gordon fields on asymptotically static spacetimes
• The holographic Hadamard condition on asymptotically Anti-de Sitter spacetimes
• Quasimodes and a lower bound for the local energy decay of the Dirac equation in Schwarzschild-Anti-de Sitter spacetime
• Explicit formula and meromorphic extension of the resolvent for the massive Dirac operator in the Schwarzschild-Anti-de Sitter spacetime