Local energy decay of massive Dirac fields in the 5D Myers-Perry metric

Abstract

We consider massive Dirac fields evolving in the exterior region of a 5-dimensional Myers-Perry black hole and study their propagation properties. Our main result states that the local energy of such fields decays in a weak sense at late times. We obtain this result in two steps: first, using the separability of the Dirac equation, we prove the absence of a pure point spectrum for the corresponding Dirac operator; second, using a new form of the equation adapted to the local rotations of the black hole, we show by a Mourre theory argument that the spectrum is absolutely continuous. This leads directly to our main result.

40 pages

References in corpus (8)

• Brane-World Gravity
• Higher-Dimensional Black Holes: Hidden Symmetries and Separation of Variables
• Quasi-normal modes and exponential energy decay for the Kerr-de Sitter black hole
• Black Holes at the LHC
• Decay of Dirac Massive Hair in the Background of Spherical Black Hole
• 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
• Creation of fermions by rotating charged black-holes
• Inverse scattering at fixed energy in de Sitter-Reissner-Nordström black holes

Cited by in corpus (5)

• The Scattering of Dirac Spinors in Rotating Spheroids
• Slowly damped quasinormal modes of the massive Dirac field in d-dimensional Tangherlini spacetime
• Solutions of the massive Dirac equation in the near-horizon metric of the extremal five dimensional Myers-Perry black hole with equal angular momenta
• Local Dirac energy decay in the 5D Myers-Perry geometry using an integral spectral representation for the Dirac propagator
• The Dirac equation across the horizons of the 5D Myers-Perry geometry : Separation of variables, radial asymptotic behaviour and Hamiltonian formalism