On the local energy decay of solutions of the Dirac equation in the non-extreme Kerr-Newman metric, I

TL;DR

This paper proves that solutions to the Dirac equation in a non-extreme Kerr-Newman black hole spacetime exhibit local energy decay over time, using spectral analysis and the RAGE theorem.

Contribution

It establishes the selfadjointness of the Dirac operator in this setting and demonstrates energy decay in the exterior region of the black hole.

Findings

Energy of Dirac solutions decays in time mean outside the event horizon

Dirac operator is selfadjoint in a suitable Hilbert space

Application of the RAGE theorem to black hole spacetime

Abstract

We investigate the local energy decay of solutions of the Dirac equation in the non-extreme Kerr-Newman metric. First, we write the Dirac equation as a Cauchy problem and define the Dirac operator. It is shown that the Dirac operator is selfadjoint in a suitable Hilbert space. With the RAGE theorem, we show that for each particle its energy located in any compact region outside of the event horizon of the Kerr-Newman black hole decays in the time mean.