Asymptotic evolution of bulk-viscous, spherically symmetric spacetimes

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.