hawkingPower
plain-language theorem explainer
Hawking power for a Schwarzschild black hole of mass M is defined as ħ c⁶ / (15360 π G² M²) using Recognition Science constants. Researchers deriving black hole evaporation rates from the J-cost functional equation and holographic ledger capacity would cite this. The definition is a direct algebraic substitution of the RS-native ħ = φ^{-5} and G = λ_rec² c³ / (π ħ) into the standard formula.
Claim. For a Schwarzschild black hole with positive mass $M$, the radiated power due to Hawking radiation is $P = ħ c^6 / (15360 π G^2 M^2)$.
background
BlackHole is a structure with a single field mass : ℝ satisfying mass > 0, representing a Schwarzschild black hole. The module derives black hole thermodynamics from Recognition Science, where horizon area measures the ledger's information capacity and temperature arises from the τ₀-scale at the horizon, targeting the Bekenstein-Hawking entropy S_BH = k_B A / (4 l_P²) and Hawking temperature T_H = ħ c³ / (8π G M k_B).
proof idea
The definition is a one-line algebraic expression that substitutes the RS-native constants ħ and G directly into the standard Hawking power formula P = ħ c⁶ / (15360 π G² M²). It relies on the upstream constant definitions without additional lemmas or tactics.
why it matters
This definition supports derivation of black hole evaporation times and information preservation in the Recognition Science framework, filling the QG-001 and QG-002 targets for holographic entropy and thermal radiation. It connects to the phi-ladder through ħ = φ^{-5} and G = φ^5 / π, and to the RCL via the underlying J-cost functional equation. No downstream uses are recorded yet.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.