hawkingTemperature
plain-language theorem explainer
The definition supplies the Hawking temperature T_H = ħ c³ / (8π G M k_B) for a Schwarzschild black hole of mass M. Researchers deriving black hole thermodynamics from information-theoretic principles would reference this when connecting the Recognition Science ledger to semiclassical gravity. It is expressed directly as an algebraic combination of the RS-native constants ħ, G, k_B and the black hole mass field.
Claim. For a Schwarzschild black hole with positive mass $M$, the Hawking temperature is $T_H = ħ c^3 / (8 π G M k_B)$.
background
The Quantum.BekensteinHawking module targets derivation of black hole thermodynamics from Recognition Science, with core results that entropy scales with horizon area and temperature is inversely proportional to mass. The BlackHole structure is defined by a positive real mass field M representing a Schwarzschild black hole. Upstream constants supply G in the form λ_rec² c³ / (π ħ) from first principles and ħ = φ^{-5} in RS units, together with the Boltzmann constant k_B.
proof idea
The definition is a direct one-line algebraic expression that substitutes the standard Hawking formula using the imported constants G, ħ, c, k_B and the mass field from the BlackHole structure.
why it matters
This definition feeds the theorems temperature_from_surface_gravity and temperature_inverse_mass, which establish equivalence to surface gravity and the inverse-mass scaling. It fills the QG-002 target for deriving Hawking temperature from the Recognition Science framework, supporting the holographic principle where entropy scales with area. It connects to the broader chain by providing the thermodynamic temperature from the ledger capacity.
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