Hawking Radiation and Superradiance in Hairless Black Holes

We explore the relationship between Hawking radiation and superradiance in black holes without hair (i.e., rotating or charged black holes carrying no additional fields). Focusing on Kerr (rotating, uncharged) and Reissner-Nordstr\"{o}m (charged, non-rotating) black holes, we derive Hawking radiation expressions using the mathematical framework of superradiant scattering. By substituting black hole parameters (such as horizon angular velocity or electric potential) into key equations, we demonstrate that the Hawking emission spectrum can be understood as a form of spontaneous superradiance. In particular, near-horizon dimensional reduction techniques show that the quantum Hawking flux emerges to cancel gravitational and gauge anomalies, analogous to the classical wave amplification in superradiance. We emphasize this connection by deriving the Hawking emission formula with rotational and electrostatic potentials, highlighting that modes satisfying the superradiant condition $\omega < m\Omega_H + q\Phi_H$ correspond to stimulated emission. We include illustrative equations and a comparative table of Kerr and Reissner-Nordstr\"{o}m parameters, and we discuss stability considerations. In Kerr black holes, thermodynamic phase transitions (inferred via thermodynamic geometry) are linked to the existence of potential barriers or wells outside the horizon, delineating regimes of superradiant stability. In charged black holes, we examine the phenomenon of "tachyonic superradiance," wherein a would-be scalar hair condensate (driven by a tachyonic instability) is entirely radiated away by superradiant emission, leaving a hairless final state. Our conclusions reinforce that Hawking radiation is closely related to superradiance\cite{Chen2021}, and together these processes play complementary roles in energy extraction from black holes while preserving the no-hair property.