Addendum to “Absorption of a massive scalar field by a charged black hole”

In [1] we studied the absorption cross section of a scalar field of mass $m$ impinging on a static black hole of mass $M$ and charge $Q$. We presented numerical results using the partial-wave method, and analytical results in the high- and low-frequency limit. Our low-frequency approximation was only valid if the (dimensionless) field velocity $v$ exceeds $v_c=2\pi Mm$. In this addendum we give the complementary result for $v\lesssim v_c$, and we consider the possible physical relevance of this regime.

Figure 1

Comparison between the partial absorption cross section ${\sigma }_{l=0}$ (solid line), and the approximate analytical results of Eq. (1) (broken lines), for the case $Q/M=0.4$ and $Mm=0.022$. A transition in behavior is visible near $v_c\approx 0.138$.