Spherically Symmetric, Self-Similar Spacetimes

TL;DR

This paper demonstrates that spherically symmetric, self-similar spacetimes necessarily have a separable metric form, are uniquely characterized, and can include matter with any equation of state, relevant to cosmology and gravitational collapse.

Contribution

It proves that self-similarity in spherically symmetric spacetimes implies metric separability and uniqueness, expanding understanding of their geometric and physical properties.

Findings

Self-similar spherically symmetric spacetimes have separable metrics.

Such spacetimes are uniquely characterized by a specific metric form.

They can include matter with arbitrary equations of state.

Abstract

Self-similar spacetimes are of importance to cosmology and to gravitational collapse problems. We show that self-similarity or the existence of a homothetic Killing vector field for spherically symmetric spacetimes implies the separability of the spacetime metric in terms of the co-moving coordinates and that the metric is, uniquely, the one recently reported in [cqg1]. The spacetime, in general, has non-vanishing energy-flux and shear. The spacetime admits matter with any equation of state.