Thermodynamic Regulation of Superradiance in a Charged Two-Dimensional Black Hole

Abstract

Within the framework of gravitational thermodynamicization, we investigate the propagation of charged scalar fields in static two-dimensional black-hole spacetimes. Starting from the scalar-field action, we derive the exact radial wave equation and show that a neutral, massless, minimally coupled scalar field in a genuinely two-dimensional geometry exhibits neither an angular-momentum barrier nor superradiant amplification. For a charged scalar field, the condition for amplification is governed by the electrostatic potential evaluated at the event horizon. In the case of the charged two-dimensional string black hole, the horizon electrostatic potential is directly related to the Hawking temperature, implying that the superradiant frequency window is determined by the thermodynamic state of the black hole. We further formulate a near-horizon residue criterion that provides a coordinate-independent characterization of the superradiant threshold. When a reflecting outer boundary is imposed, necessary frequency conditions for unstable modes are derived, together with an upper bound on their growth rates. Numerical calculations verify the corresponding flux relation and clearly distinguish superradiant scattering from genuine superradiant instability.