IndisputableMonolith.Relativity.Compact.BlackHoleEntropy
This module defines the horizon area for Schwarzschild black holes and constructs Bekenstein-Hawking entropy from ledger capacity in the Recognition Science setting. Quantum gravity and black hole thermodynamics researchers would cite these constructions when linking classical metrics to recognition ledger limits. The module consists of definitions together with short lemmas on positivity, uniqueness, and saturation.
claimHorizon area $A_H = 4 \pi r_s^2$ for Schwarzschild radius $r_s$, with entropy $S = A_H/4$ obtained from ledger capacity bounds.
background
The module belongs to the Relativity.Compact section and imports the fundamental RS time quantum $ au_0 = 1$ tick from Constants together with the Metric module for spacetime geometry. It introduces HorizonArea as the area of the event horizon for a Schwarzschild black hole and supplies supporting lemmas on ledger capacity limits and saturation properties.
The local setting is static spherically symmetric solutions whose entropy is derived from recognition ledger capacity rather than from the area law alone.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the black hole entropy constructions that feed the parent Compact module, which treats static spherically symmetric solutions and derives Bekenstein-Hawking entropy from ledger capacity. It advances the recognition framework treatment of compact objects by connecting entropy directly to ledger limits.
scope and limits
- Does not treat rotating or charged black holes.
- Does not incorporate quantum corrections to the entropy formula.
- Does not derive the metric from the recognition forcing chain.
- Does not address information loss or unitarity questions.