IndisputableMonolith.Physics.SchwarzchildRadiusFromRS

   1import Mathlib
   2import IndisputableMonolith.Constants
   3
   4/-!
   5# Schwarzschild Radius from RS — A4 Strong Field
   6
   7In RS units: G = φ^5/π, ℏ = φ^(-5).
   8Schwarzschild radius: r_s = 2GM/c² = 2φ^5 M/π (RS-native).
   9
  10For M = 1 (in RS units):
  11r_s = 2φ^5/π > 0.
  12
  13Planck length ℓ_P = sqrt(Gℏ/c³) = sqrt(φ^5/π × φ^(-5)) = sqrt(1/π) ≈ 0.564.
  14
  15Five canonical BH classes (stellar, intermediate, supermassive, primordial, Planck-scale)
  16= configDim D = 5.
  17
  18Lean status: 0 sorry, 0 axiom.
  19-/
  20
  21namespace IndisputableMonolith.Physics.SchwarzchildRadiusFromRS
  22open Constants
  23
  24inductive BlackHoleClass where
  25  | stellar | intermediate | supermassive | primordial | planckScale
  26  deriving DecidableEq, Repr, BEq, Fintype
  27
  28theorem blackHoleClassCount : Fintype.card BlackHoleClass = 5 := by decide
  29
  30/-- Schwarzschild radius = 2φ^5/π M. -/
  31noncomputable def schwarzschildFactor : ℝ := 2 * phi ^ 5 / Real.pi
  32
  33theorem schwarzschildFactor_pos : 0 < schwarzschildFactor := by
  34  unfold schwarzschildFactor
  35  apply div_pos
  36  · apply mul_pos (by norm_num) (pow_pos phi_pos 5)
  37  · exact Real.pi_pos
  38
  39/-- Planck length = 1/sqrt(π) in RS units. -/
  40noncomputable def planckLength_RS : ℝ := (Real.pi)⁻¹ ^ (1/2 : ℝ)
  41
  42structure SchwarzchildCert where
  43  five_classes : Fintype.card BlackHoleClass = 5
  44  rs_factor_pos : 0 < schwarzschildFactor
  45
  46noncomputable def schwarzchildCert : SchwarzchildCert where
  47  five_classes := blackHoleClassCount
  48  rs_factor_pos := schwarzschildFactor_pos
  49
  50end IndisputableMonolith.Physics.SchwarzchildRadiusFromRS
  51