Effective Action and Thermodynamics of Radiating Shells in General Relativity

TL;DR

This paper derives an effective action for radiating self-gravitating shells in general relativity, linking their dynamics to thermodynamic principles and providing a simplified, quasi-static description consistent with junction conditions.

Contribution

It introduces a mini-superspace approach to model radiating shells, deriving an effective action that captures their thermodynamic behavior and invariance properties.

Findings

Effective action for radiating shells derived.

Equivalence to junction equations established.

Thermodynamic interpretation of shell dynamics proposed.

Abstract

An effective action is obtained for the area and mass aspect of a thin shell of radiating self-gravitating matter. On following a mini-superspace approach, the geometry of the embedding space-time is not dynamical but fixed to be either Minkowski or Schwarzschild inside the shell and Vaidya in the external space filled with radiation. The Euler-Lagrange equations of motion are discussed and shown to entail the expected invariance of the effective Lagrangian under time-reparametrization. They are equivalent to the usual junction equations and suggest a macroscopic quasi-static thermodynamic description.