Asymptotic evolution of bulk-viscous, spherically symmetric spacetimes

TL;DR

This paper classifies kinematic self-similar solutions for spherically symmetric spacetimes with bulk viscous fluids, revealing their role as asymptotic attractors in gravitational dynamics.

Contribution

It provides a systematic classification of the most general kinematic self-similar solutions with bulk viscosity in spherically symmetric spacetimes.

Findings

Classification of kinematic self-similar solutions

Identification of solutions as asymptotic attractors

Extension of self-similarity concepts to viscous fluids

Abstract

The scale-free nature of gravitational interaction in both Newtonian gravity and the general theory of relativity gives rise to the concept of self-similarity, where solutions are scale invariant. As a result of this property, the governing partial differential equations are greatly simplified and can be transformed into ordinary ones. These solutions function as attractors, characterizing the asymptotic dynamics of more general solutions. There exist situations in which self-similarity is only partially realized, giving rise to kinematic self-similar solutions. Our study provides a systematic classification of kinematic self-similar solutions corresponding to the most general spherically symmetric spacetime in the presence of bulk viscous flows.