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

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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