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

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 not equal 0) perturbations in the RN metric. The influences of Q, e, the momentum quantum number 1, and the mode number n are discussed. Among the conclusions, the most important one is that, at the stage of quasinormal ringing, 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, which may be helpful in the astronomical observation. In addition, we compare the influence from the charge of the black hole to the spin 1/2 field and scalar field perturbations including the extremal limit (M = Q) and find a turning point of Q exists in both cases. The explanation of this fact is unclear with some suggestions that may be helpful are given.