Local Dirac energy decay in the 5D Myers-Perry geometry using an integral spectral representation for the Dirac propagator

Abstract

We consider the massive Dirac equation in the exterior region of the 5-dimensional Myers-Perry black hole. Using the resulting ODEs obtained from the separation of variables of the Dirac equation, we construct an integral spectral representation for the solution of the Cauchy problem with compactly supported smooth initial data. We then prove that the probability of presence of a Dirac particle to be in any compact region of space decays to zero as $t\to \infty$, in analogy with the case of the Dirac operator in the Kerr-Newman geometry.

Minor corrections and improvements, published version, 15 pages

References in corpus (2)

• 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
• Scattering for massive Dirac fields on the Kerr metric

Cited by in corpus (2)

• The Fermionic Entanglement Entropy of the Vacuum State of a Schwarzschild Black Hole Horizon
• The Dirac equation across the horizons of the 5D Myers-Perry geometry : Separation of variables, radial asymptotic behaviour and Hamiltonian formalism