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

TL;DR

This paper analytically investigates superradiant scattering of charged scalar fields around rotating charged de Sitter black holes in two gravity theories, revealing significant suppression of superradiance in conformal Weyl gravity compared to General Relativity.

Contribution

It introduces a novel analytical approach using Heun equations and WKB methods to compare superradiant effects in GR and CWG for charged scalar fields.

Findings

Superradiant amplification is suppressed in CWG relative to GR.

Exponential suppression of superradiance in the massive sector, proportional to e^{-2μΛ^{-1/2}}.

Analytical solutions for superradiance using Heun equations and WKB approximations.

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 $e^{-2\mu\Lambda^{-1/2}}$ in the cosmological region.