Decay of spin-1/2 field around Reissner-Nordstrom black hole

TL;DR

This paper investigates how the charge of a Reissner-Nordstrom black hole affects the decay of spin-1/2 fields, revealing that like charges accelerate decay while opposite charges slow it down during quasinormal ringing.

Contribution

It provides a detailed analysis of how black hole charge and field charge influence quasinormal mode decay rates for neutrino and massless Dirac fields.

Findings

Like charges ($eQ>0$) lead to faster decay of modes.

Opposite charges ($eQ<0$) result in slower decay.

Black hole charge significantly affects quasinormal mode evolution.

Abstract

To find what influence the charge of the black hole $Q$ will bring to the evolution of the quasinormal modes, we calculate the quasinormal frequencies of the neutrino field (charge $e=0$) perturbations and those of the massless Dirac field ($e\neq 0$) perturbations in the RN metric. The influences of $Q$, $e$, the momentum quantum number $l$, and the mode number $n$ are discussed. Among the conclusions, the most important one is that, at the stage of quasinormal ringing, the larger when the black hole and the field have the same kind of charge ($eQ>0$), the quasinormal modes of the massless charged Dirac field decay faster than those of the neutral ones, and when $eQ<0$, the massless charged Dirac field decays slower.