Relativistic Black Hole Mechanics in Covariant Bitemporal Geometrodynamics: Nonsingular Interior Σ₄ Topology, Quasinormal Ringdown Echoes, Kaluza–Klein Photon Sub-Ring Holonomy, and the 5.20 × 10¹⁰ M☉ Ultramassive Ceiling

Classical (3+1)-dimensional General Relativity (GR) predicts that gravitational collapse inevitably terminates in geodesic incompleteness and infinite curvature invariants (r → 0), while semi-classical Hawking evaporation across static event horizons (r_s = 2GM/c²) violates quantum unitarity (S S† ≠ I) and triggers inner Cauchy horizon mass-inflation instabilities in rotating Kerr geometries. Building upon the foundational principles of Covariant Bitemporal Geometrodynamics (CBG) [Paper I, DOI: 10.5281/zenodo.23443512], we present a comprehensive, first-principles mathematical and astrophysical treatise on black hole mechanics on the 5-dimensional pseudo-Riemannian manifold M_{3,2} with exterior metric signature (-,-,+,+,+). By coupling the relativistic Schutz–Clebsch velocity-potential fluid action to the bitemporal dilaton field Φ(x^A) governed by the universal topological vacuum expectation value Φ_∞ = Ω/c = 2.40 × 10⁻⁴ (Ω = 71.95 km/s, Φ_∞² = 5.76 × 10⁻⁸), we prove that all classical black hole pathologies are resolved without free parameters. Specifically, we demonstrate that: (1) Exact Event-Horizon Geodesic Regularity: As the Gullstrand–Painlevé spatial inflow velocity approaches the speed of light at the horizon (σ(r) = v²/c² = r_s/r → 1), the conserved Noether bitemporal overflow momentum Ω produces an exact algebraic cancellation of the (r - r_s)² geodesic divergence, yielding a finite inward horizon-crossing acceleration a_Ω = -Ω²c²/(4GM) and regularizing the 5D Kretschmann curvature invariant K_5(r) at the Planck boundary layer δr = L_P. (2) Interior Signature Flip and Nonsingular Σ_4 Topology: Inside the horizon (0 < r < r_s, where σ > 1), Φ(r)² inverts sign and induces a smooth metric signature flip (-,-,+,+,+) → (-,+,+,+,+), converting the secondary time coordinate t_2 into a compact fourth spatial dimension w = ct_2 on a 4-dimensional spatial hypersurface Σ_4 ≃ R_r × S¹_w × S² stabilized at a nonsingular Planck core (r_core ≥ L_P, ρ_max = ρ_P, K_5(0) = 192/L_P⁴ < ∞). (3) 5D Kerr–Bitemporal Rotating Black Holes: Extending M_{3,2} to axisymmetric rotating black holes in Doran–Painlevé coordinates with rotational saturation σ_Kerr(r,θ) = r_s r / (r² + a² cos²θ) proves that the bitemporal saturation surface (σ_Kerr = 1) coincides with the Kerr ergosphere r_erg(θ), eliminating both the Kerr ring singularity and the inner Cauchy horizon mass-inflation instability. (4) Quasinormal Ringdown Shift and Gravitational-Wave Echoes: Linearization of the 5D Einstein–Jiménez–Velasco field equations yields modified Regge–Wheeler and Zerilli master perturbation equations predicting a universal fractional shift in quasinormal mode frequencies (Δω_QNM / ω_QNM^(GR) = +½ Φ_∞² = +2.88 × 10⁻⁸) and delayed gravitational-wave ringdown echoes governed by the parameter-free scaling law Δt_echo(M) = (2r_s/c)[ln(r_s/2L_P) + 1/2] ≈ 1.800 ms × (M/M_☉) (Δt_echo = 54.0 ms for M = 30 M_☉ and 129.8 ms for GW150914). (5) Berry–Kaluza–Klein Photon Sub-Ring Holonomy: Null rays orbiting the modified photon sphere r_phot^(CBG) = (3/2)r_s(1 - ⅓ Φ_∞²) acquire an achromatic Berry–Kaluza–Klein polarization rotation (EVPA holonomy shift) of Δχ_pol = Φ_∞ = 49.50 arcseconds per half-orbit on demagnified VLBI sub-rings (n ≥ 2), testable with the Black Hole Explorer (BHEX). (6) Unitary Hawking Evaporation and 703.2 PeV Threshold: Bitemporal Bogoliubov quantization on H_{t1} ⊗ H_{t2} bounds the Hawking temperature to T_max^(CBG) = T_P/(6√3 π) ≈ 5.52 × 10³⁰ K, halts evaporation at a stable zero-temperature Planckian remnant M_rem = m_P/2 = 1.088 × 10⁻⁸ kg, and defines a 703.2 PeV/c² bitemporal Kaluza–Klein excitation threshold. (7) Sgr A* 6.90 pc Halo Knee, JWST High-Redshift Seeds, and the 5.20 × 10¹⁰ M_☉ Quasar Ceiling: On astrophysical scales, the bitemporal halo truncation law R_trunc = r_s / Φ_∞² = 1.736 × 10⁷ r_s predicts the exact 6.903 pc dynamical transition radius of the Milky Way Nuclear Star Cluster around Sgr A*, accelerates high-redshift (z > 10) JWST black hole seed growth (τ_Salp^(CBG) = 33.75 Myr, reproducing UHZ1 at z = 10.1), and establishes an absolute theoretical upper limit for luminous black hole accretion at M_max = 3Ω³/(8π G H_0) = 5.20 × 10¹⁰ M_☉, matching the observed ultramassive quasar ceiling (TON 618 and Phoenix A).