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 regular de Sitter interior from a Schwarzschild or Schwarzschild–de Sitter exterior in a post-transient regime with fixed exterior mass M (ADM for ${\mathrm{\Lambda }}_{+}=0$), modelling a vacuum–energy core surrounded by an asymptotically classical spacetime. The configuration admits a natural thermodynamic interpretation based on a geometric area functional $S_{\mathrm{shell}}\propto R^2$ and Tolman redshift, both derived from classical junction conditions and used as an entropy-like coarse-grained quantity rather than a fundamental statistical entropy. Key results include (i) identification of a deceleration mechanism at the balance radius $R_{\mathrm{thr}}={(3M/{\mathrm{\Lambda }}_{-})}^{1/3}$ for linear surface equations of state $p=w\sigma$; (ii) classification of the allowable radial domain $V\left(R\right)\le 0$ for outward evolution; (iii) bounded curvature invariants throughout the shell-supported spacetime region; and (iv) a mass-scaled frequency bound $f_c{R}_S\le \xi /\left(3\sqrt{3}\pi \right)$ 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 thin-shell collapse dynamics within classical general relativity, with implications for alternative compact object scenarios.