Scalar absorption by charged rotating black holes

We compute numerically the absorption cross section of planar massless scalar waves impinging upon a Kerr-Newman black hole with different incidence angles. We investigate the influence of the black hole electric charge and angular momentum in the absorption spectrum, comparing our numerical computations with analytical results for the limits of high and low frequency.

Figure 1

LEFT: We plot $-M^2{V}_{\omega lm}$ as a function of $r$ for a fixed value of the BH angular momentum, $a=0.8M$, and different values of BH charge-to-mass ratio, $q\equiv Q/M$. RIGHT: The function $-M^2{V}_{\omega lm}$ is plotted for $q=0.3$ and different values of $a$. For both cases, we choose $M\omega =0.1$ and $l=m=1$.

Figure 2

LEFT: The capture cross section for a fixed value of the rotation parameter ($a=0.9M$) and different values of the charge-to-mass ratio ($q=0$, 0.1, 0.2, and 0.3). RIGHT: The capture cross section for a fixed value of the BH charge ($q=0.3$) and different values of the BH rotation ($a/M=0$, 0.3, 0.6, and 0.9).

Figure 3

LEFT: The total absorption cross section for a fixed BH rotation, $a=0.9M$, with $q=0$, 0.1, 0.2, and 0.3. RIGHT: The total absorption cross section for a BH charge $q=0.3$ and different rotation parameters $a/M=0$, 0.3, 0.6, and 0.9. Both left and right panels were obtained for on-axis incidences ($\gamma =0$), and the horizontal lines are the capture cross sections of null geodesics in each case.

Figure 4

LEFT: The total absorption cross section for incidences along the equatorial plane for $a=0.8M$, and $q=0.1$, 0.3, and 0.5. RIGHT: The total absorption cross section for $\gamma =90\mathrm{deg}$, with $q=0.3$, and different BH rotations $a/M=0.3$, 0.6, and 0.9. The horizontal lines are the values of the capture cross section for null geodesics in each case.

Figure 5

LEFT: The corotating (${\sigma }^{co}$) and counterrotating (${\sigma }^{\text{counter}}$) contributions to the absorption cross section for $a=0.8M$ and $q=0.1$, 0.3, and 0.5. RIGHT: The corotating and counterrotating contributions to the absorption cross section for $q=0.3M$ and $a/M=0.3$, 0.6, and 0.9.

Figure 6

LEFT: Counterrotating ($m=-1$) and corotating ($m=1$) partial absorption cross sections for $\gamma =60\mathrm{deg}$; $a=0.9M$; and $q=0.1$, 0.2, and 0.3. RIGHT: Counterrotating and corotating partial absorption cross sections for a fixed BH charge ($q=0.3$) and different rotation parameters $a/M=0.3$, 0.6, and 0.9. We consider $\gamma =60\mathrm{deg}$. In both the right and left panels, the curves associated to the higher peaks are related to the counterrotating modes, while the low peaks are associated to corotating ones.

Figure 7

LEFT: The partial absorption cross section for the mode $l=m=1$ with $a=0.9M$, and $q=0.1$ and 0.3. RIGHT: The partial absorption cross section for the mode $l=m=1$, with $q=0.1$, and $a/M=0.9$ and 0.99. In both the left and right panels, the insets help one see more clearly the superradiance, which is very small for scalar waves.