Inverse Time Limit Theory (ITLT): Minimal Singularity-Free Spacetime from Curvature Saturation in Einstein Gravity: Black Hole, Cosmology, Charged & Rotating Extensions, and Information Paradox

# Inverse Time Limit Theory (ITLT) — Version 2.0 (Extended) ## 📌 OverviewThis is the extended version (v2.0) of the Inverse Time Limit Theory (ITLT), originally submitted to EPJC. The theory proposes that spacetime curvature cannot grow without bound but saturates at a fundamental density scale ρ₊ = βMₚ⁴. This principle of *curvature saturation* yields a minimal, nonsingular extension of Einstein gravity without introducing exotic matter or modifying the Einstein–Hilbert action. ## 🔬 Key Results ### 🕳️ Black Hole Sector- Static spherically symmetric solution: f(r) = 1 − 2Mr²/(r³ + a) with a = M/ρ₊- Replaces classical Schwarzschild singularity with a regular de Sitter core- All curvature invariants (Ricci, Kretschmann) remain finite everywhere- Geodesic completeness proven analytically- Linear stability established (axial + polar perturbations)- Thermodynamics with quantum-corrected entropy: S = πrₕ² − 2πa/rₕ + S₀- Stable Planck‑mass remnants predicted ### ⚡ Charged Extension- Metric includes charge regularization: F(r) = 1 − 2Mr²/(r³+a) + Q²/r² · r⁴/(r⁴+b)- Regular de Sitter core preserved- Linear stability verified for 0 ≤ Q ≤ 0.9- Entropy contains additional −2πb/rₕ³ term ### 🌪️ Rotating Extension- Kerr‑like metric with mass function M(r) = Mr³/(r³ + l), l = M/ρ₊- Regular core replaces Kerr ring singularity- Horizon structure, ergosphere, and shadow computed- Shadow radius for a=0.5, l=0.5: α = 4.965 (4.46% smaller than Schwarzschild)- Testable with ngEHT ### 🔥 Information Paradox Resolution- Evaporation stops at extremal mass, leaving stable remnants- Page curve saturates at S₍rem₎ = S₀, preserving unitarity- Information stored in correlations between remnant and radiation- No exotic matter or extra dimensions required ### 🌌 Cosmology- Modified Friedmann equation: H² = (8πG/3) ρ (1 − ρ/ρ₊)- Nonsingular bounce replaces big bang singularity- Maximum Hubble rate: Hₘₐₓ = √(β/12) Mₚ- Tensor‑to‑scalar ratio bound: β ≲ 4×10⁻⁹ ## 📊 Testable Predictions- Shadow radius: ~4.3% (static) and ~4.46% (rotating) smaller than Schwarzschild- QNM frequencies: ℜ(ω) ≈ 0.55 vs Schwarzschild 0.374- Echo time delay: Δt ∼ few ms for M ∼ 10M☉- Planck‑mass remnants as dark matter candidates ## 📁 Contents- `ITLT_Paper.pdf` — Complete paper (20 sections, 60 pages, 10 figures, 22 references)- `ITLT_Paper.tex` — LaTeX source- `ITLT.bib` — BibTeX references- `figures/` — All 10 plots (metric, curvature, horizons, temperature, stability, cosmology, geodesics, shadow)- `README.md` — This information- `LICENSE` — MIT License- `CITATION.cff` — Citation metadata ## 📜 LicenseThis work is licensed under the MIT License. ## 📧 ContactAbhay Piya — abhaypiya69@gmail.com ORCID: 0009-0007-6739-4787 ## 🔗 Related- Version 1.0 (EPJC submission) available separately