Absorption cross section of electromagnetic waves for Schwarzschild black holes

The absorption cross section of black holes has been investigated for various fields. Nevertheless, the absorption cross section of Schwarzschild black holes for the electromagnetic field has been only calculated in the low- and high-frequency approximations until now. Here we compute it numerically for arbitrary frequencies.

Figure 1

The partial electromagnetic absorption cross section ${\sigma }_E^{(l)}$ is plotted as a function of the wave frequency $\omega$ for $l=1$ up to $l=6$. We note that the larger $l$ is, the smaller is the maximum of the corresponding ${\sigma }_E^{(l)}$.

Figure 2

The total absorption cross sections for the electromagnetic case ${\sigma }_E$ and massless scalar case ${\sigma }_S$ are plotted as functions of the frequency $\omega$. The summation in the angular momentum is performed up to $l=6$. We see that for high frequencies they oscillate around the limit of geometrical optics ${\sigma }_O\equiv 27\pi M^2$. We also plot ${\sigma }_E^{(\omega \approx 0)}$ calculated analytically [see Eq. (25)] to show that this is in agreement with our numerical calculation.