Quasi-homologous evolution of self-gravitating systems with vanishing complexity factor
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Regular Article - Theoretical Physics
Quasi-homologous evolution of self-gravitating systems with vanishing complexity factor L. Herrera1,a , A. Di Prisco2,b , J. Ospino3,c 1
Instituto Universitario de Física Fundamental y Matemáticas, Universidad de Salamanca, Salamanca 37007, Spain Escuela de Física, Facultad de Ciencias, Universidad Central de Venezuela, Caracas 1050, Venezuela 3 Departamento de Matemática Aplicada and Instituto Universitario de Física Fundamental y Matemáticas, Universidad de Salamanca, Salamanca 37007, Spain
2
Received: 27 May 2020 / Accepted: 3 July 2020 © The Author(s) 2020
Abstract We investigate the evolution of self-gravitating either dissipative or non-dissipative systems satisfying the condition of minimal complexity, and whose areal radius velocity is proportional to the areal radius (quasi-homologous condition). Several exact analytical models are found under the above mentioned conditions. Some of the presented models describe the evolution of spherically symmetric dissipative fluid distributions whose center is surrounded by a cavity. Some of them satisfy the Darmois conditions whereas others present shells and must satisfy the Israel condition on either one or both boundary surfaces. Prospective applications of some of these models to astrophysical scenarios are discussed.
1 Introduction In a recent paper [1] a concept aiming to asses the degree of complexity of a self-gravitating spherically symmetric static fluid distribution was introduced with the hope that the variable defining such property could help to deepen in the study of self-gravitating systems. This definition was latter on extended to the time dependent case [2], which required the introduction of a criterium for a definition of the simplest pattern of evolution. The presented arguments in [2] strongly suggested that the homologous condition seemed to be the most suitable to describe the simplest mode of evolution. The applications of this concept including systems with different kind of symmetry and/or other theories of gravity, may be found in [3–21] and references therein.
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In this work we are concerned with the problem of general relativistic gravitational collapse under the assumption of vanishing complexity factor. The relevance of the study of gravitational collapse in astrophysics is illustrated by the fact, that the gravitational collapse of massive stars represents one of the few observable phenomena where general relativity is expected to play a relevant role. Ever since the early work by Oppenheimer and Snyder [22], much has been done by researchers trying to provide models of evolving self–gravitating spheres. However this endeavour proved to be difficult and uncertain. Thus, while it is true that numerical methods enable researchers to investigate systems which are extremely difficult to handle analytically, it is also true t
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