Horizon brightened acceleration radiation from massive vector fields

Abstract

In this paper, we develop a quantum-optical treatment of acceleration radiation for atoms freely falling into a Schwarzschild black hole when the ambient field is a massive spin-1 (Proca) field. Building on the HBAR framework of Scully and collaborators, we analyze two detector realizations: a charged-monopole current coupling and a physical electric-dipole coupling, both within a cavity that isolates a single outgoing Schwarzschild mode prepared in the Boulware state. Using a near-horizon stationary-phase analysis, we show that the thermal detailed-balance factor governing excitation versus absorption is universal and depends only on the near-horizon Rindler coordinate transformation. At the same time, the absolute spectra acquire distinctive Proca signatures: a hard mass threshold, polarization-dependent prefactors, and axial/polar graybody transmissions. Promoting single-pass probabilities to escaping rates yields a master equation whose steady state is geometric and whose entropy flux obeys an horizon brightened acceleration radiation-style area-entropy relation identical in form to the scalar case, with all vector-field specifics entering through the radiative area change. Our results provide a controlled pathway to probe longitudinal versus transverse responses, mass thresholds, and the role of polarization-resolved graybody transmission in acceleration radiation. More precisely, we derive the universal near-horizon kernel and show how the Proca transmission data enter the escaping probabilities, rates, and entropy flux; a dedicated numerical computation of the axial/polar graybody profiles is left for future work. This sets the stage for extensions to rotating backgrounds, alternative exterior states, and detector-engineering strategies.