Kerr Black Hole Interior Cosmology: The Perspective Effect, Coordinate-Independent Acceleration, and Fibonacci Redshift Quantization as a Geometric Alternative to Dark Energy

We derive three independent cosmological results directly from the interior geometry of a rotating Kerr black hole, using only the Goldberg–Sachs theorem, the Raychaudhuri equation, the Poisson–Israel mass inflation instability, and the KAM theorem — without postulating new fields, modified gravity, or any additional metric structure.
The first result is the Perspective Effect: the principal null congruences of the Kerr interior carry identically vanishing shear, and frame-dragging conservation preserves azimuthal geodesic spreading while mass-inflation focusing collapses one polar transverse dimension. This reduces the effective luminosity distance scaling from (1+z) to (1+z)^(1/2), modifying the apparent continuity equation to ρ̇ + 2H(ρ+p) = 0 without violating local energy conservation.
The second result is coordinate-independent cosmic acceleration. The frame-dragging coupling amplitude γ = (m₀/M)·2r₋²/(r₋²+a²) is derived from the mass inflation perturbation of the inner horizon radius. An explicit transformation to standard cosmic time proves ä(τ) > 0 at all late epochs, establishing acceleration as a geometric consequence of the Kerr interior independent of any cosmological constant.
The third result is Fibonacci Temporal Quantization. Action-variable analysis of null geodesic orbits near the Cauchy horizon shows the winding number ratio equals κ₋/ω₋, where κ₋ is the surface gravity and ω₋ the frame-dragging frequency. By the KAM theorem the last surviving invariant torus has winding ratio equal to the golden ratio φ = (1+√5)/2, constraining the parent black hole spin to a/M ≈ 0.7035 and predicting discrete redshift shells at zₙ = φⁿ − 1. The self-consistency of this structure requires the fundamental identity H₀ = κ₋: the Hubble constant equals the Cauchy-horizon surface gravity. The first shell at z₁ ≈ 0.618 naturally coincides with the observed onset of cosmic acceleration. An effective interior metric encoding all three results is presented as a derived summary. Joint analysis against Pantheon+ and DESI BAO data is statistically competitive with ΛCDM.