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This theoretical framework explores nonsingularity and remnant properties of black holes, implying new insights into cosmic dynamics.
General relativity describes the exterior geometry of black holes with extraordinary success; yet at the centre it leaves a curvature singularity, the one signalled by the Hawking–Penrose theorems. This paper binds the black hole to a single identity within the ΨD (Dimensional Flow Cosmology) framework: the black hole is the local, density-triggered instance of the cosmic return. Matter in the d3 phase descends through the d2 and d1 rungs into a finite d0 Planckon core; the process is the planckon ledger — E(d) = (d+1)ε_P, U(d) = (3−d)ε_P, E+U = 4ε_P — run in reverse: collapse is not a loss of energy but the re-loading of unfolded energy into closed potential. Five main results are established. (i) The core radius is derived from the effective Planck density: r₁ = ℓ_P[(3/4π)(M/m_P)]^(1/3); the critical mass ratio satisfying r₁ = r_s is √(3/32π) ≈ 0.1727 (M_thr ≈ 3.76 µg). (ii) Nonsingularity is ontological: since the separation set is discrete, “r→0” cannot be constructed; the force saturates at F_P = c⁴/G and the curvature at a mass-independent universal Planck-order ceiling — K ≤ 48(4π/3)²/ℓ_P⁴ ≈ 8.4×10²/ℓ_P⁴; the vacuum expression terminates at the core surface r₁ and M cancels completely — and geodesic completeness holds without any additional mechanism. (iii) By the mass–excess accounting, the core potential is exactly U_core = Mc²; the energy condition for rebound reduces to η > 1/2 and coincides precisely with the lower edge of the efficiency window (1/2 < η < 1) derived along an independent second route — the leak-covering condition. (iv) The remnant theorem: at astrophysical masses r₁/r_s ~ 10⁻²⁶–10⁻³³, so the geometric escape condition fails categorically; large black holes are non-exploding, externally classical Planckon-cored remnants — rebound is possible only at M ~ m_P. (v) The exterior Schwarzschild geometry is supported by the weak-field spin-2 layer of the bond network (coupling 8πG/c⁴), and the Deser premises are satisfied from within the framework; N_c = M/(3m_P) is a matter count, not an entropy (N_c ∝ √S). All epistemic statuses are collected in a single table (Section 11).
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Hamdi Barut (2026) studied this question.
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