The state space and physical interpretation of self-similar spherically symmetric perfect-fluid models

TL;DR

This paper explores the solution space of self-similar spherically symmetric perfect-fluid models, combining state space and physical quantities to understand their physical interpretation and implications for gravitational collapse.

Contribution

It introduces a unified approach to analyze different classes of self-similar models, including inhomogeneous, quasi-static, and Minkowski asymptotics, with insights into gravitational collapse and naked singularities.

Findings

Models asymptotically approach Friedmann solutions

Identification of conditions for naked singularity formation

Connection between self-similar solutions and critical collapse behavior

Abstract

The purpose of this paper is to further investigate the solution space of self-similar spherically symmetric perfect-fluid models and gain deeper understanding of the physical aspects of these solutions. We achieve this by combining the state space description of the homothetic approach with the use of the physically interesting quantities arising in the comoving approach. We focus on three types of models. First, we consider models that are natural inhomogeneous generalizations of the Friedmann Universe; such models are asymptotically Friedmann in their past and evolve fluctuations in the energy density at later times. Second, we consider so-called quasi-static models. This class includes models that undergo self-similar gravitational collapse and is important for studying the formation of naked singularities. If naked singularities do form, they have profound implications for the predictability of general relativity as a theory. Third, we consider a new class of asymptotically Minkowski self-similar spacetimes, emphasizing that some of them are associated with the self-similar solutions associated with the critical behaviour observed in recent gravitational collapse calculations.