IndisputableMonolith.Gravity.HawkingTemperatureSI
SI packaging of Schwarzschild Hawking temperature: exact Boltzmann constant, kelvin-scale $T_H$, and SI Schwarzschild radius, obtained by pushing the RS-native rung formula through the dimensional bridge. Gravity and quantum-gravity tracks cite it whenever temperatures or horizons must sit in laboratory units. Content is definitions plus bridge equalities and positivity lemmas.
claimIn SI units the module fixes the exact Boltzmann constant $k_B$, defines the Hawking temperature $T_H^{\mathrm{SI}}(M)$ of a Schwarzschild black hole of mass $M$ and the SI Schwarzschild radius $r_s^{\mathrm{SI}}(M)$, proves both are positive for $M>0$, and records the bridge identities equating the geometric (RS-native) and SI presentations of $T_H$.
background
Recognition Science states Hawking temperature first in RS-native units, where the structural identity is fixed by rung spacing on the $\phi$-ladder (Track G2). That native formula lives in HawkingTemperatureFromRung and is conditional only on the same dimensional bridge that ties $M_Z$ to GeV.
The SI bridge closure supplies the unique calibration map from RS-native units to SI once the dimensional anchor is fixed. This module applies that map and inserts the 2019-exact Boltzmann constant so temperatures appear in kelvin.
Local objects are therefore $k_B^{\mathrm{SI}}$, $T_H^{\mathrm{SI}}$, and $r_s^{\mathrm{SI}}$, together with the two directions of the bridge equality between geometric and SI temperatures.
proof idea
Definition-and-bridge module rather than a deep derivation. Constants and temperature/radius maps are introduced by def; positivity follows from positivity of the native formula and of the bridge factors; the two bridge lemmas are one-line transports of the native Hawking identity through SIBridgeClosure. No independent continuum GR calculation is performed here.
why it matters in Recognition Science
Feeds BlackHoleEntropySI (Track 3.B), which needs SI temperature to state black-hole entropy and discriminator margins against LQG and string theory in laboratory units. Also imported by MasterTheorem (Track 7.A), the conditional gravity master statement that aggregates the closed tracks. Without this SI layer the native rung formula cannot be compared to measured kelvin scales or to the SI form of the Bekenstein-Hawking area law. Sits downstream of the T5-T8 forcing chain only indirectly, via the native Hawking identity and the unique SI calibration map.
scope and limits
- Does not re-derive Hawking radiation from continuum QFT on curved spacetime.
- Does not fix the dimensional bridge; it consumes SIBridgeClosure as a black box.
- Does not treat Kerr, Reissner-Nordström, or other non-Schwarzschild horizons.
- Does not prove numerical agreement with a specific astrophysical temperature measurement.
- Does not close black-hole entropy; that is deferred to BlackHoleEntropySI.
used by (2)
depends on (2)
declarations in this module (25)
-
def
k_B_SI -
theorem
k_B_SI_pos -
def
T_hawking_SI -
theorem
T_hawking_SI_def -
theorem
hawking_temperature_SI -
theorem
T_hawking_SI_pos -
theorem
T_hawking_SI_strict_anti -
theorem
T_hawking_SI_eq_geom_via_bridge -
theorem
T_hawking_geom_eq_SI_via_bridge -
def
schwarzschildRadius_SI -
theorem
schwarzschildRadius_SI_def -
theorem
schwarzschildRadius_SI_pos -
theorem
T_hawking_SI_eq_inv_schwarzschildRadius -
def
t_Page_SI -
theorem
t_Page_SI_def -
def
K_Page_SI -
theorem
K_Page_SI_pos -
theorem
t_Page_SI_eq_K_mul_M_cube -
theorem
t_Page_SI_pos -
theorem
t_Page_SI_strict_mono -
theorem
t_Page_SI_squared_planck_form -
structure
HawkingTemperatureSICert -
def
hawkingTemperatureSICert -
theorem
hawkingTemperatureSICert_inhabited -
theorem
hawking_temperature_SI_one_statement