Absorption of electromagnetic plane waves by rotating black holes

We study the absorption of monochromatic electromagnetic plane waves impinging upon a Kerr black hole, in the general case that the direction of incidence is not aligned with the black hole spin axis. We present numerical results that are in accord with low- and high-frequency approximations. We find that circularly polarized waves are distinguished by the black hole spin, with counter-rotating polarizations being more absorbed than co-rotating polarizations. At low frequencies and moderate incidence angles, there exists a narrow parameter window in which superradiant emission in the dipole mode can exceed absorption in the non-superradiant modes, allowing a planar electromagnetic wave to stimulate net emission from a black hole.

Figure 1

Left: Monochromatic wave of angular frequency $\omega$ impinges upon a Kerr black hole of mass $M$ and angular momentum $J$ at an angle of $\gamma$ relative to the spin axis. Right: Geodesic capture cross section ${\sigma }_{\mathrm{geo}}$ as a function of the angle of incidence $\gamma$ for various spin rates $a\equiv J/M$.

Figure 2

Transmission factors for different angular modes. The plot shows the transmission factors for the angular modes $l=3$ and $-l\le m\le +l$ as functions of $\omega M$, considering a Kerr BH with $a=0.9M$.

Figure 3

Absorption cross sections ${\sigma }_{\mathrm{abs}}$ as a function of $M\omega$ for circularly polarized electromagnetic waves incident parallel to the black hole rotation axis, showing the co-rotating (left) and counter-rotating (right) helicities. The five series correspond to rotation parameters $a=0$ (Schwarzschild BH), $0.4M$, $0.8M$, $0.9M$, and $0.99M$.

Figure 4

Electromagnetic absorption at low frequencies. The plot shows the absorption cross section ${\sigma }_{\mathrm{abs}}$ divided by $\frac{4}{3}\mathcal{A}{\mathrm{\Omega }}_{H}M$, where $\mathcal{A}$ and ${\mathrm{\Omega }}_H$ are the area and angular frequency of the event horizon, respectively [cf. Eq. (1)]. The thick dashed lines are for the co-rotating polarization, for BH spin ratios of $a=0.4M$, $a=0.8M$, $a=0.9M$ and $a=0.99M$. The thick solid lines, which overlie each other, are for the counter-rotating polarization for the same values of $a$. The thin dotted lines show the approximations $-\omega (1-\omega /{\mathrm{\Omega }}_H)$.

Figure 5

Absorption cross sections for co-rotating (left) and counter-rotating (right) circular polarizations, for angles of incidence $\gamma =10°$, 45°, 80° and 90°. The cross section becomes more irregular as the angle of incidence increases. In the case of equatorial incidence ($\gamma =90°$) there is no difference between the cross sections of the two circular polarizations (co- and counter-rotating).

Figure 6

Partial absorption cross sections ($l=m=1$) for different incidence angles ($\gamma =0°$, 10°, 45°, 80°, and 90°) and $a=0.99M$. Superradiance is larger for on-axis incidence.

Figure 7

Absorption cross sections for linearly polarized electromagnetic waves. Absorption is larger the smaller the value of the BH rotation parameter. As well as in the case of circularly polarized waves, the absorption cross sections present a less regular behavior for off-axis incidences.

Figure 8

Comparison of the results for linearly, co-rotating, and counter-rotating polarized incident electromagnetic waves.