Collapsing Spheres Satisfying An "Euclidean Condition"

TL;DR

This paper investigates fluid sphere models satisfying the Euclidean condition where area and radius are equal, exploring both dissipative and non-dissipative cases, and deriving specific solutions with unique physical properties.

Contribution

It introduces a class of solutions satisfying the Euclidean condition, including a subclass of Lemaitre-Tolman-Bondi models and characterizes dissipative solutions with uniform radial acceleration.

Findings

Non-dissipative models are necessarily geodesic.

Dissipative models exhibit non-geodesic motion with uniform radial acceleration.

A subclass of solutions corresponds to Lemaitre-Tolman-Bondi models.

Abstract

We study the general properties of fluid spheres satisfying the heuristic assumption that their areas and proper radius are equal (the Euclidean condition). Dissipative and non-dissipative models are considered. In the latter case, all models are necessarily geodesic and a subclass of the Lemaitre-Tolman-Bondi solution is obtained. In the dissipative case solutions are non-geodesic and are characterized by the fact that all non-gravitational forces acting on any fluid element produces a radial three-acceleration independent on its inertial mass.