Spherical symmetric parabolic dust collapse: ${\cal C}^{1}$ matching metric with zero intrinsic energy

TL;DR

This paper explores a class of spherical dust collapse models by matching interior and exterior solutions with ${ m C}^1$ continuity, analyzing their intrinsic energy to identify physically plausible models.

Contribution

It introduces a novel approach by starting from exact solutions and applying ${ m C}^1$ matching conditions, providing a new perspective on dust collapse modeling.

Findings

Derived a family of models satisfying ${ m C}^1$ matching conditions.

Identified models with finite, constant intrinsic energy as physically plausible.

Explored implications of matching conditions on collapse dynamics.

Abstract

The collapse of marginally bound, inhomogeneous, pressureless (dust) matter, in spherical symmetry, is considered. The starting point is not, in this case, the integration of the Einstein equations from some suitable initial conditions. Instead, starting from the corresponding general exact solution of these equations, depending on two arbitrary functions of the radial coordinate, the fulfillment of the Lichnerowicz matching conditions of the interior collapsing metric and the exterior Schwarzschild one is tentatively assumed (the continuity of the metric and its first derivatives on the time-like hypersurface describing the evolution of the spherical 2-surface boundary of the collapsing cloud), and the consequences of such a tentative assumption are explored. The whole analytical family of resulting models is obtained and some of them are picked out as physical better models on the basis of the finite and constant value of its {\em intrinsic} energy.