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

## TL;DR

This paper studies gravitational collapse using thin-shell models in general relativity, linking classical dynamics to thermodynamic concepts.

## Contribution

A novel thermodynamic interpretation of thin-shell collapse is introduced using geometric area and Tolman redshift as entropy-like quantities.

## Key findings

- A deceleration mechanism is identified at a critical radius for specific surface equations of state.
- The radial domain for outward evolution is classified based on junction conditions.
- Curvature invariants remain bounded in the shell-supported spacetime region.

## Abstract

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 Λ+=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 Sshell∝R2 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 Rthr=(3M/Λ−)1/3 for linear surface equations of state p=wσ; (ii) classification of the allowable radial domain V(R)≤0 for outward evolution; (iii) bounded curvature invariants throughout the shell-supported spacetime region; 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 thin-shell collapse dynamics within classical general relativity, with implications for alternative compact object scenarios.

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Source: https://tomesphere.com/paper/PMC12840486