Scattering of charged massive scalar waves by Kerr-Newman black holes

TL;DR

This work extends scattering theory to equatorial incidence of charged massive scalar waves by Kerr-Newman black holes, employing a partial-wave framework with a series-reduction technique to control forward divergences. By systematically varying BH rotation $a$, charge $Q$, and field parameters $q$, $\mu$, and $\omega$, the authors map out how frame-dragging, electromagnetic interactions, and superradiance sculpt the equatorial differential cross section $\frac{d\sigma}{d\Omega}$, revealing that frame-dragging drags the glory away from exact backward directions and that mass and Lorentz repulsion modulate fringe structure and flux. In slow rotation, increasing $Q$ or $q$ broadens fringes and enhances forward flux, while in rapid rotation the cross section becomes more irregular but still shows fringe shifts; superradiance further amplifies the cross section in prograde regions and can trigger substantial amplification for large $q$. These equatorial-plane signatures distinguish charged, rotating spacetimes from axis-axis analyses and sharpen understanding of how BH parameters imprint on wave scattering.

Abstract

The scattering of charged massive scalar waves by Kerr-Newman black holes, with incidence along the equatorial plane, is investigated in this work. The differential scattering cross section is computed using the partial wave method, with the forward divergence handled via the series reduction technique. For the first time, we systematically examine the influence of the black hole charge, electromagnetic interactions, and field mass on the equatorial cross section. Our results reveal that regardless of whether the electromagnetic interaction is present or not, the frame-dragging effect shifts the glory away from the exact backward direction and can place interference minima there, contrasting with the on-axis scattering case. The average scattered flux intensity at the medium to large scattering angles exhibits a large enhancement as the Lorentz attraction or field mass increases, particularly in the slowly rotating regime, with the enhancement being frequency-dependent. When superradiance occurs, we observe that the cross section in the prograde scattering angles ($\sim 135^{\circ} < φ< 270^{\circ}$) increases as the black hole spin increases, due to enhanced prograde partial wave contributions. Meanwhile, the superradiant scattering cross section increases in all (except the forward) directions when the Lorentz force becomes more repulsive. These findings highlight unique equatorial-plane signatures of charged, rotating spacetimes, distinguishing them from prior on-axis analyses.

Figures (7)

• Figure 1: Comparison of the cross sections at $\theta=\pi/2$, computed using the series reduction and amplitude decomposition methods, for the incoming direction $(\gamma, \phi_0) = (\pi/2, \pi/2)$. The insets show the cross sections in the range $150^\circ < \phi < 170^\circ$ to highlight the differences more clearly.
• Figure 2: The cross sections for fixed parameters $a=0.4,\, q=0.5,\, Q=0.6,\,\mu=0.2$ and $\omega=1$, for scalar waves incident from $(\gamma,\phi_0)=(\pi/3,\pi/4)$ (top) and $(\pi/2,\pi/2)$ (bottom).
• Figure 3: The cross section as a function of $\phi$ at fixed $\theta = \pi/2$ for neutral massive scalar fields scattered by a KN BH with different values of $a$. The incident wave propagates along $(\gamma, \phi_0) = (\pi/2, \pi/2)$. Left: slowly rotating case; right: rapidly rotating case.
• Figure 4: The cross section as a function of $\phi$ at fixed $\theta=\pi/2$ for neutral massive scalar fields scattered by a KN BH with different values of $Q$. The incident wave propagates along $(\gamma, \phi_0) = (\pi/2, \pi/2)$. Left: slowly rotating case; right: rapidly rotating case.
• Figure 5: The cross section as a function of $\phi$ at fixed $\theta=\pi/2$ for a charged massive scalar field scattered by a slowly rotating KN BH, shown for different values of $a$ (top left), $Q$ (top right and bottom right), $q$ (middle left), $\mu$ (middle right), and $\omega$ (bottom left). The incident wave propagates along $(\gamma, \phi_0) = (\pi/2, \pi/2)$.