Late-time evolution of charged massive Dirac fields in the Reissner-Nordströmblack-hole background

The late-time evolution of the charged massive Dirac fields in the background of a Reissner-Norström (RN) black hole is studied. It is found that the intermediate late-time behavior is dominated by an inverse power-law decaying tail without any oscillation in which the dumping exponent depends not only on the multiple number of the wave mode but also on the field parameters. It is also found that, at very late times, the oscillatory tail has the decay rate of $t^{-5/6}$ and the oscillation of the tail has the period $2\pi /\mu$ which is modulated by two types of long-term phase shifts.

Figure 1

Graphs of $\ln |G^C(r_{*},r_{*}^{\prime };t)|$ versus $t$ for different $seQ$. These figures show that the dumping exponent depends on the product of the spin weight and the charges of the black hole and Dirac fields, and $seQ<0$ speeds up the perturbation decay but $seQ>0$ slows it down.

Figure 2

Graphs of $\ln |G^C(r_{*},r_{*}^{\prime };t)|$ versus $t$ for different $\lambda$ with $s=\pm 1/2$, $\mu =0.01$ and $eQ=0.01$, showing that the dumping exponent depends on the multiple number of the wave mode, and the larger the magnitude of multiple number, the more quickly the perturbation decays.

Figure 4

Graphs of $\ln |G^C(r_{*},r_{*}^{\prime };t)|$ versus $t$ with $M=100$, $\mu =0.01$, $s=-1/2$, $\lambda =1$, $Q=0.1M$ and $e=0.002$ for the first term (solid line). The dashed line is $\sim \log |1/t|$.

Figure 5

Graphs of $\ln |G^C(r_{*},r_{*}^{\prime };t)|$ versus $t$ with $M=100$, $\mu =0.01$, $s=-1/2$, $\lambda =1$, $Q=0.1M$ and $e=0.002$ for the second term (solid line). The dashed line is $\sim \log |t^{-5/6}|$.