A Horizon-as-Apparatus Model That Reproduces Black Hole Thermodynamics

Area of Science:

• Black hole thermodynamics
• Quantum field theory
• Information theory

Background:

• The Bekenstein-Hawking area law describes black hole entropy (SBH) as proportional to the event horizon area (A).
• A precise statistical interpretation of the SBH = A/(4ℓp²) formula, particularly the 1/4 factor, remains an active area of research.
• Understanding the quantum nature of black hole horizons is crucial for unifying general relativity and quantum mechanics.

Purpose of the Study:

• To present a measurement-driven model where the black hole horizon acts as a classical apparatus.
• To provide a concrete statistical interpretation of the Bekenstein-Hawking area law and its 1/4 factor.
• To explore the information-theoretic bookkeeping of quantum field modes at the horizon.

Main Methods:

• Modeling the black hole horizon as a classical apparatus with Planck-scale patches as quantum field mode detectors.
• Calculating the thermal ensemble generated by each patch (approximately 0.25 nat per mode).
• Summing contributions from area-scaling patches to determine total black hole entropy.

Main Results:

• The model successfully reproduces the Bekenstein-Hawking area law (SBH = A/4ℓp²).
• Quantum simulations with a realistic Hawking spectrum yielded an average entropy ⟨Sk⟩ = 0.257 nat.
• The study provides a statistical interpretation for the 1/4 factor in the entropy formula.

Conclusions:

• The horizon-as-apparatus mechanism offers a novel approach to understanding black hole entropy.
• The model adheres to established principles, offering a statistical interpretation rather than a first-principles derivation.
• Testable predictions for analogue systems are outlined, facilitating experimental verification.