Ringdown modulation of acceleration radiation in the Schwarzschild background (2511.03766v1)

Abstract: We present an analytic, first-order description of how black hole ringdown imprints on the operational signature of near-horizon thermality. Building on a static Schwarzschild baseline in which a freely falling two-level system coupled to a single outgoing mode exhibits geometric photon statistics and a detailed-balance ratio set by the surface gravity, we introduce an even-parity, axisymmetric quadrupolar perturbation and work in an ingoing Eddington-Finkelstein, horizon-regular framework. The perturbation corrects the outgoing eikonal through a gauge-invariant double-null contraction of the metric, yielding a compact redshift map that, when pulled back to the detector worldline, produces a universal, decaying-oscillatory modulation of the Boltzmann exponent at the quasinormal frequency. We derive a closed boundary formula for the response coefficient at the sampling radius, identify the precise adiabatic window in which the result holds, and prove that the modulation vanishes in all stationary limits. Detector specifics (gap, switching wavepacket width) enter only through a smooth prefactor, while the geometric content is captured by the quasinormal pair and the response coefficient. The analysis clarifies that near-horizon "thermality" is robust but not rigid: detailed balance persists as the organizing structure and is gently driven by ringdown dynamics. The framework is minimal yet extensible to other multipoles, parities, and slow rotation, and it suggests direct numerical and experimental cross-checks in controlled analog settings.