module module high

`IndisputableMonolith.Gravity.UltramassiveBH`

The module defines black hole structures in RS-native units with base length and time quanta set to unity and c equal to 1. It supplies RSBH together with the Schwarzschild radius, horizon area, cell count, entropy, and Hawking temperature built from the J-cost function. Gravity researchers working inside the Recognition Science derivation would cite these for black hole thermodynamics. The content consists of definitions and elementary lemmas on positivity and bounds.

claimThe RS black hole RSBH with mass parameter $M$ has Schwarzschild radius $r_s = 2M$, horizon area $A = 4π r_s^2$, entropy $S = A/4$, and Hawking temperature $T_H = 1/(8π M)$ in units where $ℓ_0 = τ_0 = c = 1$.

background

Recognition Science derives all physical laws from a single functional equation whose solution yields the J-cost $J(x) = (x + x^{-1})/2 - 1$. The Constants module fixes the RS time quantum at $τ_0 = 1$ tick. JcostCore supplies the core J-cost definitions and the Recognition Composition Law $J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y)$. This module applies those tools to ultramassive black holes, introducing RSBH as the native black hole object and deriving its geometric and thermodynamic quantities from the J-cost lower bound.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The module supplies the black hole definitions required by the gravity sector of the Recognition framework. It connects the J-cost lower bound to horizon entropy and temperature, supporting the derivation of classical gravity from the forcing chain steps T5 through T8 that fix $D = 3$ spatial dimensions and the eight-tick octave. No downstream theorems are listed yet, indicating this is foundational scaffolding for black hole thermodynamics in RS units.

scope and limits

Does not derive the Einstein equations from the J-cost functional equation.
Does not treat charged or rotating black holes.
Does not compute the mass spectrum for ultramassive objects.
Does not address information loss or unitarity issues.
Does not provide numerical predictions for specific astrophysical black holes.

depends on (2)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import
IndisputableMonolith.Cost.JcostCore module_import

declarations in this module (26)

structure RSBH L44
def schwarzschildRadius L49
def horizonArea L53
def k_R L58
lemma k_R_pos L60
def horizonCells L63
def rs_entropy L68
def rs_hawkingTemp L74
theorem Jcost_finite_on_pos L81
theorem Jcost_zero_iff_one L88
theorem Jcost_lower_bound L108
theorem nothing_costs_arbitrarily_large L117
theorem rs_entropy_eq L138
theorem rs_entropy_pos L142
theorem entropy_quadruples_on_double L153
theorem rs_hawkingTemp_pos L163
theorem temp_decreases_with_mass L171
theorem temp_halves_on_double L180
theorem hamiltonian_approximation_bound L202
theorem small_strain_hamiltonian_valid L208
def phiRung L217
theorem phi_ladder_recovery L221
theorem cosmic_censorship_automatic L236
theorem bh_interior_finite_cost L242
structure UltramassiveBHCert L254
def ultramassiveBHCert L264