Superradiant Suppression of Non-minimally Coupled Scalar fields for a Rotating Charged dS Black Hole in Conformal Weyl Gravity

Abstract

In this study, we present an analytical investigation of the superradiant scattering of a massive charged conformally coupled scalar field in rotating charged $de~Sitter$ black hole spacetimes within two gravitational theories: General Relativity (GR) and fourth-order Conformal (Weyl-squared) Gravity (CWG). For the massless charged conformally coupled scalar, we exploit a recently discovered correspondence between the Heun equation and the semiclassical limit of Belavin-Polyakov-Zamolodchikov (BPZ) equations in two-dimensional conformal field theory to solve for the superradiant amplification factors as controlled expansions in a small parameter scaling. For the massive charged conformally coupled scalar, we use WKB methods to derive an order of magnitude approximation for the amplification factors in the cosmological region in terms of those in the region $r_+\ll r \ll r_c$ where $r_+$ and $r_c$ are the outer and cosmological event horizons, respectively. For both the massless and massive sectors, suppression of superradiant amplification in CWG relative to that in GR is observed across the parameter regimes studied. Particularly, in the massive sector, we find strong exponential suppression of superradiant amplification on the order of $e^{-2μΛ^{-1/2}}$ in the cosmological region.

Figures (12)

• Figure 1: Parameter space (a, $\Lambda$) for the $KNdSCG$ (Panel (a)) and $KNdS$ (Panel (b)) spacetimes. The region bounded by the blue and red curves in the lower left corner denotes the black hole region with at least one event horizon. The red curve indicates $r_E=r_{E,c}$ where the cosmological ergosphere and the black hole ergosphere coincide. To its right side, the black hole no longer possesses an ergosphere. For both cases: $Q=0.5$.
• Figure 2: Parameter space (Q, $\Lambda$) for the $KNdSCG$ (Panel (a)) and $KNdS$ (Panel (b)) spacetimes. The region bounded by the blue and red curves in the lower left corner denotes the black hole region with at least one event horizon. The red curve indicates $r_E=r_{E,c}$ where the cosmological ergosphere and the black hole ergosphere coincide. To its right side, the black hole no longer possesses an ergosphere. For both cases: $a/M=0.5$.
• Figure 3: Outer event horizon, $r_{+}$, as a function of $Q/M$ (Panel (a)) and $a/M$ (Panel (b)). In both graphs, the solid lines represent the $KNdSCG$ spacetime and the dashed lines represent the $KNdS$ spacetime.
• Figure 4: $r_{ISCO}$ as a function of $Q/M$ (Panel (a)) and $a/M$ (Panel (b)). In both graphs, the solid lines represent the $KNdSCG$ spacetime and the dashed lines represent the $KNdS$ spacetime.
• Figure 5: Meridional cross section of the ergoregion for varying $a/M$ (Panel (a)) and $Q/M$ (Panel (b)). In both graphs, the solid lines represent the $KNdSCG$ spacetime and the dashed lines represent the $KNdS$ spacetime.