Complexity and simplicity of self-gravitating fluids

TL;DR

This paper reviews a new definition of complexity for self-gravitating fluids, explores its applications in gravitational collapse, and establishes a hierarchy of solutions from simplest to most complex.

Contribution

It introduces a novel complexity measure for self-gravitating fluids and extends its application to various symmetries and vacuum solutions in general relativity.

Findings

Exact solutions for minimal complexity static fluids are presented.

A complexity hierarchy from Minkowski to radiating systems is established.

The concept of quasi-homologous evolution broadens solution possibilities.

Abstract

We review a recently proposed definition of complexity of the structure of self--gravitating fluids \cite{ch1}, and the criterium to define the simplest mode of their evolution. We analyze the origin of these concepts and their possible applications in the study of gravitation collapse. We start by considering the static spherically symmetric case, extending next the study to static axially symmetric case. Afterward we consider the non--static spherically symmetric case. Two possible modes of evolution are proposed to be the simplest one. One is the homologous conditio,, however, as was shown later on, it may be useful to relax this last condition to enlarge the set of possible solutions, by adopting the so-called quasi-homologous condition. As another example of symmetry, we consider fluids endowed with hyperbolical symmetry. Exact solutions for static fluid distributions satisfying the condition of minimal complexity are presented.. An extension of the complexity factor to the vacuum solutions of the Einstein equations represented by the Bondi metric is discussed. A complexity hierarchy is established in this case, ranging from the Minkowski spacetime (the simplest one) to gravitationally radiating systems (the most complex). Finally we propose a list of questions which, we believe, deserve to be treated in the future