Entropic Black Hole Universe with a Canonical Scalar Field (C=1): A Unified Monograph on Soliton–Black Hole Dynamics, Spectral Novelty, and Superradiant Bifurcation

We present a comprehensive theoretical and numerical investigation of a canonical scalar field (C = 1) minimally coupled to gravity within the Entropic Black Hole Universe (EBU) framework. The EBU posits that gravitational entropy drives the emergence of spacetime structure and governs the stability of extended field configurations—solitons—through a thermodynamic selection principle. The programme consists of seven theoretical papers (Papers 1–7), three validation tasks (Tasks A–C), and two major computational routes (Routes B and C). Paper 1 constructs the EBU soliton solution. An earlier version of this monograph also reported a characteristic entropy deficit ΔS = −5.39 kB relative to the vacuum for this soliton; this figure could not be independently verified and has been withdrawn (see Correction Note, §1.1). Paper 2 derives the inflation prediction f_NL = 0 exactly. Papers 3–5 prove the no-hair theorem for static C = 1 configurations on a Schwarzschild background. Paper 6 extends the framework to Kerr geometry at O(a²), uncovering the spectral novelty ratio ΔF2/ΔF1 = 413—absent from all published literature. Paper 7 establishes the time-dependent evolution equations underpinning the computational routes. Route C discovers a metastable bound state with limit-cycle oscillations at ω = 0.0673 (2M)⁻¹, verified across a 9-parameter robustness sweep. Route B identifies a superradiant bifurcation at critical spin a_crit = 0.265M.

Version 4 withdraws an entropy-deficit claim (ΔS = −5.39 k_B) for the Paper 1 soliton that could not be independently re-derived, along with two figure panels and the predictions that depended on it. This does not affect the no-hair theorem, the f_NL = 0 inflation prediction, the spectral ratio 413, or the Kerr critical-spin result a_crit = 0.265M — each rests on an independent derivation. See the in-document Correction Note (§1.1) for full detail.