arXiv:2511.03766v1 Announce Type: new
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.
Conclusions and Future Roadmap
The analysis presented in this study provides a detailed understanding of how black hole ringdown affects the operational signature of near-horizon thermality. The framework developed in this research sheds light on the interaction between ringdown dynamics and the geometric content of black hole thermality.
Roadmap for Readers
- Explore the implications of the perturbation on the eikonal behavior and redshift map.
- Investigate the universal modulation of the Boltzmann exponent at the quasinormal frequency.
- Examine the closed boundary formula for the response coefficient and its implications.
- Identify the adiabatic window in which the results hold and understand its significance.
- Consider the implications for stationary limits and the persistence of detailed balance.
- Explore the potential for extending the framework to other multipoles, parities, and slow rotation.
- Investigate numerical and experimental cross-checks in controlled analog settings.
Potential Challenges and Opportunities
Challenges:
- Complex mathematical formalism may require specialized expertise to fully understand and apply.
- Experimental verification of the theoretical predictions may pose technical challenges.
Opportunities:
- Potential for further advancements in understanding black hole thermodynamics and dynamics.
- Exploration of new avenues for experimental validation of theoretical predictions.