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

TL;DR

This paper proves that massive Dirac fields in the exterior of a 5D Myers-Perry black hole exhibit weak local energy decay at late times, using spectral analysis and Mourre theory.

Contribution

It demonstrates the absolute continuity of the Dirac operator spectrum and establishes local energy decay for massive Dirac fields in a 5D black hole background.

Findings

Local energy of Dirac fields decays weakly at late times

Dirac operator spectrum is absolutely continuous

No pure point spectrum for the Dirac operator

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.