Scattering for massive Dirac fields on the Kerr metric

Abstract

Starting with the Dirac equation outside the event horizon of a non-extreme Kerr black hole, we develop a time-dependent scattering theory for massive Dirac particles. The explicit computation of the modified wave operators at infinity is done by implementing a time-dependent logarithmic phase shift from the free dynamics to offset the long range term in the full Hamiltonian due to the presence of the gravitational force. Analytical expressions for the wave operators are also given.

33 pages, 1 figure, new proof of Lemma III.1, minor changes in Section III, a few typos corrected in Thm. IV.1 and Thm. B.3

References in corpus (4)

• Non-Existence of Time-Periodic Solutions of the Dirac Equation in an Axisymmetric Black Hole Geometry
• On the Eigenvalues of the Chandrasekhar-Page Angular Equation
• Scattering of massive Dirac fields on the Schwarzschild black hole spacetime
• The Dirac propagator in the Kerr-Newman metric

Cited by in corpus (9)

• Separability of the massive Dirac's equation in 5-dimensional Myers-Perry black hole geometry and its relation to a rank-three Killing-Yano tensor
• The massive Dirac field on a rotating black hole spacetime: Angular solutions
• Sharp decay estimates for massless Dirac fields on a Schwarzschild background
• The Massive Dirac Equation in the Kerr Geometry: Separability in Eddington-Finkelstein-type Coordinates and Asymptotics
• Quantum Field Theory in Curved Spacetime (2nd Edition)
• Local Dirac energy decay in the 5D Myers-Perry geometry using an integral spectral representation for the Dirac propagator
• Conformal scattering theory for the Dirac field on Kerr spacetime
• Conformal scattering theories for tensorial wave equations on Schwarzschild spacetime
• On the eigenvalues of the fermionic angular eigenfunctions in the Kerr metric