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September 12, 20251 citationsOpen Access

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

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ASA. Schubert

Key Points

  • A closed-form threshold for outward shell evolution was derived, balancing interior and exterior forces.
  • The analysis reveals bounded scalar curvature invariants throughout the considered spacetime, ensuring stability.
  • The model supports thermodynamic concepts like entropy-like growth, indicating classical parallels in gravitational physics.
  • Findings present a horizon-free scenario for late-time collapse in GR, avoiding curvature singularities and focusing issues.

Abstract

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.

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Cite This Study

A. Schubert (2025) studied this question.

synapsesocial.com/papers/68d44a3031b076d99fa53226https://doi.org/10.20944/preprints202509.0991.v1
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