Timelike Thin-Shell Evolution in Gravitational Collapse: Classical Dynamics and Thermodynamic Interpretation

This work explores late-time gravitational collapse using timelike thin-shell methods in classical general relativity. A junction surface separates a de Sitter interior from a Schwarzschild or Schwarzschild–de Sitter exterior in a post-transient regime with fixed exterior mass M (ADM for Λ+=0). The configuration exhibits thermodynamic properties including area–entropy scaling S∝R2 and Tolman redshift, derived entirely from classical junction conditions. Key results include: (i) identification of a deceleration mechanism at the balance radius Rthr=(3M/Λ−)1/3 for linear equations of state p=wσ, (ii) classification of the allowable radial domain V(R)≤0 for outward evolution, (iii) bounded curvature invariants throughout the covered spacetime domain, and (iv) a mass-scaled frequency bound fcRS≤ξ/(33π) for persistent near-shell spectral modes. All predictions follow from standard Israel junction techniques and provide concrete observational tests. The framework offers an analytically tractable example of regular collapse dynamics within classical general relativity, with implications for alternative compact object scenarios.