Dirac dynamical resonance states around Schwarzschild black holes

TL;DR

This paper explores the existence, construction, and evolution of Dirac dynamical resonance states around Schwarzschild black holes, revealing their long-term stability and decay characteristics influenced by various physical parameters.

Contribution

It introduces the concept of Dirac dynamical resonance states, constructs their stationary configurations, and analyzes their decay behavior through numerical simulations.

Findings

Energy of resonance states decays exponentially.

Decay rate depends on frequency, mass, angular momentum, and spin-orbit interaction.

Ultra-light Dirac particles can remain near black holes for cosmological timescales.

Abstract

Recently, a novel kind of scalar wigs around Schwarzschild black holes---scalar dynamical resonance states were introduced in [Phys. Rev. D 84, 083008 (2011)] and [Phys. Rev. Lett. 109, 081102 (2012)]. In this paper, we investigate the existence and evolution of Dirac dynamical resonance states. First we look for stationary resonance states of a Dirac field around a Schwarzchild black hole by using the Schr\"{o}dinger-like equations reduced from the Dirac equation in Schwarzschild spacetime. Then Dirac pseudo-stationary configurations are constructed from the stationary resonance states. We use these configurations as initial data and investigate their numerical evolutions and energy decay. These dynamical solutions are the so-called "Dirac dynamical resonance states". It is found that the energy of the Dirac dynamical resonance states shows an exponential decay. The decay rate of energy is affected by the resonant frequency, the mass of Dirac field, the total angular momentum, and the spin-orbit interaction. In particular, for ultra-light Dirac field, the corresponding particles can stay around a Schwarzschild black hole for a very long time, even for cosmological time-scales.