Infinite Kinematic Self-Similarity and Perfect Fluid Spacetimes

TL;DR

This paper investigates perfect fluid spacetimes with infinite kinematic self-similarity, analyzing their differential equations, asymptotic behavior, and exact solutions to understand their physical and geometric properties.

Contribution

It provides a detailed analysis of the differential equations governing these spacetimes, including exact solutions and their asymptotic behavior, highlighting the role of self-similarity in their structure.

Findings

Solutions exhibit specific asymptotic behaviors

Exact solutions are derived for special cases

Self-similar solutions are key to understanding spacetime dynamics

Abstract

Perfect fluid spacetimes admitting a kinematic self-similarity of infinite type are investigated. In the case of plane, spherically or hyperbolically symmetric space-times the field equations reduce to a system of autonomous ordinary differential equations. The qualitative properties of solutions of this system of equations, and in particular their asymptotic behavior, are studied. Special cases, including some of the invariant sets and the geodesic case, are examined in detail and the exact solutions are provided. The class of solutions exhibiting physical self-similarity are found to play an important role in describing the asymptotic behavior of the infinite kinematic self-similar models.