Dynamical Casimir Effect and Vacuum Friction in the Near-Horizon Geometry of a Black Hole
We investigate the Dynamical Casimir Effect (DCE) for a relativistic scalar field confined within a cavity possessing moving boundaries in the (1+1)-dimensional near-horizon geometry of a black hole. By applying a coordinate transformation, we map the moving-boundary problem to an equivalent acoustic metric with static boundaries, allowing for an exact canonical Hamiltonian formulation. We find that the local gravitational redshift fundamentally alters the vacuum structure, and the dynamical boundary motion induces time-dependent mode-mixing. When a boundary moves, it scatters the fluctuations of the ambient Hartle-Hawking state, generating a flux of created particles. Crucially, because the coordinate speed of light relative to the Killing time $t$ vanishes as one approaches the event horizon, we establish that maintaining physical, subluminal boundary motion requires the mechanical oscillation amplitude to scale proportionally with the proper distance to the horizon. Consequently, the effective Mach number of the moving mirror approaches zero in the near-horizon limit. Using a rigorous small-amplitude perturbative expansion and proper canonical operator normalization, we demonstrate that the transition probability into the field is heavily suppressed by a conformal geometric factor. Furthermore, we account for the Bose-enhancement caused by the thermal Hawking bath. While the thermal presence introduces infrared density-of-states enhancement, it remains insufficient to overcome the kinematic damping. Finally, we conclude that the extreme spacetime curvature acts to protect the near-horizon vacuum; the transition probability vanishes as the boundary approaches the event horizon, indicating a geometric and kinematic suppression of particle creation in the strong-gravity limit.