Superradiance in static black hole spacetimes

We investigate the absorption of a massive and charged scalar field in a Reissner-Nordström background. We compare our numerical results for the absorption cross section, obtained for arbitrary frequencies, with the low- and high-frequency limits. We find, in particular, that the total absorption cross section can be negative, showing that planar scalar waves can be superradiantly amplified by black holes.

Figure 1

Reflection coefficient as a function of the frequency for $M\mu =0.4$, $Q/M=0.8$, $l=0$, and different choices of $Mq$.

Figure 2

Reflection coefficient for $Q/M=0.8$, $Mq=1.6$, and different values of $M\mu$. As in Fig. 1, here we only exhibit the values of $|R_{\omega l}{|}^2$ which are greater than 1.

Figure 3

Total absorption cross section as a function of the frequency, for $M\mu =0.4$, $Q/M=0.4$, and different choices of $Mq$.

Figure 4

Total absorption cross section for $Q/M=0.4$, $Mq=1.6$, and different values of $M\mu$. As in Fig. 3, here we also exhibit the corresponding high-frequency result.

Figure 5

Comparison between the partial absorption cross section for $l=0$ (${\sigma }_0$) obtained numerically and the low-frequency approximation (${\sigma }_{lf}$) for different choices of $M\mu$. We have chosen $Q/M=0.4$ and $Mq=0.1$.

Figure 6

Partial and total absorption cross sections for $M\mu =0.4$, $Q/M=0.4$, and $Mq=-0.4$.

Figure 7

Partial and total absorption cross sections for $M\mu =0.4$, $Q/M=0.8$, and $Mq=1.6$.