temperature_inverse_mass
plain-language theorem explainer
Hawking temperature scales inversely with black hole mass under the Recognition Science derivation of black hole thermodynamics. Quantum gravity researchers and those studying holographic bounds would cite this when linking horizon ledger capacity to radiation properties. The proof is a one-line algebraic reduction that unfolds the temperature definition, substitutes the mass-doubling hypothesis, and simplifies via ring.
Claim. Let $bh_1$ and $bh_2$ be Schwarzschild black holes with positive masses $M_1$ and $M_2$ satisfying $M_1 = 2 M_2$. Then the Hawking temperatures satisfy $T_H(bh_1) = T_H(bh_2)/2$, where $T_H(M) = hbar c^3 / (8 pi G M k_B)$.
background
The module derives black hole thermodynamics from Recognition Science, targeting Bekenstein-Hawking entropy proportional to horizon area and Hawking temperature inversely proportional to mass. A BlackHole is defined as a structure with positive real mass $M$. The temperature is given explicitly by $T_H = hbar c^3 / (8 pi G M k_B)$, arising from the recognition scale at the horizon where area measures ledger information capacity. Upstream results include the dimensionless bridge $K = phi^{1/2}$ and the temperature definition itself.
proof idea
The term-mode proof unfolds the hawkingTemperature definition to expose the mass in the denominator. It rewrites using the hypothesis that the first mass equals twice the second, then applies the ring tactic to cancel common factors and produce the exact factor of one-half.
why it matters
This theorem completes the second core result listed in the module for QG-001 and QG-002, confirming inverse mass scaling for Hawking temperature in the Recognition Science account of black hole radiation. It supports the target paper proposition on Black Hole Thermodynamics from Information Theory. Within the framework it aligns with the holographic principle and the emergence of temperature from the tau_0 scale at the horizon.
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