module module moderate

`IndisputableMonolith.Physics.NoHairTheorem`

The module defines the three conserved charges forced by the Recognition Science J-cost for asymptotically flat spacetimes and shows that these charges fix the black hole state. Physicists studying black hole uniqueness theorems cite the resulting charge triple and state equivalence. The module proceeds by introducing charge and state types, then cost and entropy functions that enforce non-negativity and uniqueness.

claimAn asymptotically flat spacetime carries three RS-forced conserved charges whose values completely determine the black hole state, with the associated cost functional nonnegative and zero precisely when two states share identical charges.

background

Recognition Science derives all physics from the single functional equation whose J-cost satisfies the composition law J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y). This module imports the JcostCore definitions of that functional and applies them to black hole physics in asymptotically flat geometries. It therefore works inside the forcing chain that yields J-uniqueness, the self-similar fixed point phi, the eight-tick octave, and D = 3 spatial dimensions.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The module supplies the charge and state infrastructure that supports the black-hole entropy lemmas defined among its siblings, including bekenstein_hawking_entropy and entropy_linear_in_area. It thereby realizes the uniqueness implied by J-uniqueness (T5) for spacetime configurations and closes one concrete step of the unified forcing chain inside the Physics domain.

scope and limits

Does not treat spacetimes with nonzero cosmological constant.
Does not compute explicit numerical values for the three charges.
Does not address higher-dimensional or non-asymptotically flat geometries.
Does not incorporate quantum corrections or dynamical stability.

depends on (1)

Lean names referenced from this declaration's body.

IndisputableMonolith.Cost.JcostCore module_import

declarations in this module (17)

structure BHCharges L29
def BHState L35
def hair_cost L41
theorem hair_cost_nonneg L45
theorem hair_cost_zero_iff L53
theorem no_hair_field_decay L77
theorem bh_state_determined_by_charges L91
theorem bh_state_eq_of_charges_eq L108
def bekenstein_hawking_entropy L124
theorem entropy_nonneg L127
theorem entropy_linear_in_area L131
def schwarzschild_entropy L138
theorem schwarzschild_entropy_eq L141
theorem schwarzschild_entropy_monotone L147
def hawking_temperature L160
theorem hawking_temp_positive L163
theorem hawking_temp_decreases L169