The Post-Quasi-Static Approximation: An Analytical Approach to Gravitational Collapse

Abstract

[EN]A seminumerical approach proposed many years ago for describing gravitational collapse in the post-quasi-static approximation is modified in order to avoid the numerical integration of the basic differential equations the approach is based upon. For doing that we have to impose some restrictions on the fluid distribution. More specifically, we shall assume the vanishing complexity factor condition, which allows for analytical integration of the pertinent differential equations and leads to physically interesting models. Instead, we show that neither the homologous nor the quasihomologous evolution are acceptable since they lead to geodesic fluids, which are unsuitable for being described in the post-quasi-static approximation. Also, we prove that, within this approximaCitation: Herrera, L.; Di Prisco, A.; Ospino, J. The Post-Quasi-Static Approximation: An Analytical Approach to Gravitational Collapse. Symmetry 2024, 16, 341. https:// doi.org/10.3390/sym16030341 Academic Editors: Stefano Profumo, Sergei D. Odintsov, Sunil Kumar Tripathy, Dipanjali Behera and HoomanMoradpour Received: 9 February 2024 Revised: 23 February 2024 Accepted: 6 March 2024 Published: 12 March 2024 Copyright: © 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). tion, adiabatic evolution also leads to geodesic fluids, and therefore, we shall consider exclusively dissipative systems. Besides the vanishing complexity factor condition, additional information is required for a full description of models. We shall propose different strategies for obtaining such an information, which are based on observables quantities (e.g., luminosity and redshift), and/or heuristic mathematical ansatz. To illustrate the method, we present two models. One model is inspired in the well-known Schwarzschild interior solution, and another one is inspired in Tolman VI solution.