module module moderate

`IndisputableMonolith.Physics.NoHairTheorem`

The module defines the no-hair theorem in Recognition Science by introducing the three RS-forced conserved charges for asymptotically flat spacetimes and the associated black hole states. Physicists deriving classical GR results from the RS functional equation would cite it. The module structures its content as definitions and lemmas built directly on J-cost non-negativity from the imported JcostCore.

claimThe three RS-forced conserved charges of an asymptotically flat spacetime are denoted $BHCharges$, with black hole state $BHState$ satisfying $bh_state_determined_by_charges$ when uniquely fixed by these charges; $hair_cost onneg 0$ with equality precisely when no additional hair is present.

background

The module sits inside the Recognition Science framework for physics and imports JcostCore to access the J-cost function used for measuring deviations. The supplied module doc-comment identifies the central object as the three RS-forced conserved charges. Sibling declarations introduce $BHCharges$, $BHState$, the cost function $hair_cost$, and supporting statements on non-negativity and state uniqueness.

proof idea

this is a definition module, no proofs

why it matters in Recognition Science

The module establishes the no-hair theorem and thereby feeds the entropy results listed among its siblings, including bekenstein_hawking_entropy and entropy_linear_in_area. It supplies the black-hole uniqueness step required by the broader Recognition Science derivation that begins from the functional equation and the forcing chain.

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