Superradiant scattering by rotating black-bounce black holes

TL;DR

This paper investigates superradiant scattering off rotating regular black holes described by a Kerr-like black-bounce metric with regularization parameter $p$ and deformation exponents $(k,n)$. By solving the separated Klein-Gordon equation for massless scalars with $( ext{ell}, ext{m})=(1,1)$, the authors map the amplification factor $Z$ across the parameter space ($a/M$, $p/M$) and identify the peak amplification $ar{Z}$ and its frequency $ar{ olinebreak[0] olinebreak[0] olinebreak[0] olinebreak[0] olinebreak[0] olinebreak[0] olinebreak[0] olinebreak[0] olinebreak[0]$omega$ for each $(k,n)$. They find that while $n=1$ does not enhance superradiance beyond the Kerr maximum, configurations with $n>1$ can exceed Kerr by up to about $198rac{\%}{1}$, with enhancements tied to ultra-spinning regimes ($a/M>1$) and to the deformation parameters; increasing $k$ tends to damp the effect. These results imply that regular, Kerr-like geometries can substantially alter energy extraction via superradiance, motivating further studies of perturbations and stability in beyond-Kerr spacetimes. The work provides a quantitative framework for assessing how regular cores and metric deformations impact strong-field wave scattering in astrophysical contexts.

Abstract

We investigate superradiant scattering off a rotating regular black hole described by a black-bounce metric which generalizes the Kerr spacetime of mass $M$ and specific angular momentum $a$ through a regularization parameter $p$ and two deformation exponents $(k,n)$. Focusing on massless $(\ell,m)=(1,1)$ scalar modes, we explore the parameter space and compute amplification factors by numerically integrating the separated radial Klein-Gordon equation. We track the peak amplification and the corresponding frequency across the $(a/M,p/M)$ parameter space for several combinations of $k$ and $n$. We find that increasing $n$ systematically enhances superradiance, whereas increasing $k$ tends to suppress it. In particular, certain configurations yield amplification levels up to 98% larger than the maximum amplification for standard Kerr black holes.

Figures (3)

• Figure 1: Contour plots of the event horizon radius $r_0/M$ as a function of the parameters $a/M$ and $p/M$ for different values of the deformation exponents $k$ and $n$. Each column corresponds to a given $n \in \{1, 2, 3\}$, while each row corresponds to a given $k \in \{ 0, 1, 2, 3\}$. The panels highlight how the interplay between spin, black-bounce parameter and deformation exponents constrains the parameter space of black hole configurations.
• Figure 2: Contour plots of the relative maximum superradiant amplification $\overline{Z}/\overline{Z}^{\mathrm{Kerr}}_{\mathrm{max}}$ in the $(a/M,p/M)$ parameter space for different values of the deformation exponents $k$ and $n$. Each column corresponds to a fixed $n=1,2,3$, and each row to a fixed $k=0,1,2,3$. The color scale quantifies the enhancement or suppression of the amplification relative to the Kerr case, highlighting how deviations controlled by $p/M$ and the deformation exponents modify the efficiency of superradiant scattering. The red dot in each panel denotes the location of the global maximum $\overline{Z}_{\mathrm{max}}$.
• Figure 3: Contour plots of the frequency $M\overline{\omega}$ associated with the maximum superradiant amplification in the $(a/M,p/M)$ parameter space for different values of the deformation exponents $k$ and $n$. Each column corresponds to a fixed $n=1,2,3$, and each row to a fixed $k=0,1,2,3$. The color scale indicates the value of $M\overline{\omega}$, illustrating how the peak frequency shifts with the spin $a/M$, the black-bounce parameter $p/M$, and the deformation exponents. The red dot in each panel marks the location of the global maximum $\overline{Z}_{\mathrm{max}}$ shown in Fig. \ref{['fig:Z']}.