Timelike Thin-Shell Evolution in Gravitational Collapse: Geometric and Thermodynamic Perspectives in Classical General Relativity

Thermodynamic ideas—linking geometry, entropy, and the negative heat capacity of gravitating systems—play an increasing role in black hole physics and late-time gravitational dynamics. Motivated by this perspective, we present a conservative, fully classical analysis of spherical collapse using only standard tools from general relativity (GR), yet admitting a clear thermodynamic reading. A timelike thin shell connects a regular constant-curvature (de Sitter) interior to a Schwarzschild or Schwarzschild–de Sitter (SdS) exterior. After a brief formation stage, we focus on a post-transient regime with negligible inflow and fixed exterior mass (ADM mass if Lambda+ = 0). Casting the Israel junction condition into an effective potential, the analysis yields: (i) a closed-form sufficient threshold for outward shell evolution, balancing interior and exterior forces; (ii) bounded scalar curvature invariants throughout the covered spacetime; and (iii) a simple, falsifiable redshift bound for near-shell spectral modes, scaled by mass. Although purely geometric in derivation, these results are consistent with classical thermodynamic intuition: entropy-like area growth, energy-driven expansion, and the role of negative specific heat. The model offers a regular, horizon-free scenario for late-time collapse in classical GR, free from curvature singularities and geodesic focusing.