Dynamic model of spherical perturbations in the Friedmann universe. II. retarding solutions for the ultrarelativistic equation of state

TL;DR

This paper derives and analyzes exact linear retarding spherical solutions to Einstein's equations around a Friedmann universe with an ultrarelativistic equation of state, establishing their uniqueness.

Contribution

It provides the first detailed derivation and proof of uniqueness for retarding solutions in this cosmological context.

Findings

Exact linear retarding solutions are obtained.

Solutions are proven to be unique in the C^1 class.

The solutions describe spherical perturbations in the Friedmann universe.

Abstract

Exact linear retarding spherically symmetric solutions of Einstein equations linearized around Friedmann background for the ultrarelativistic equation of state are obtained and investigated. Uniqueness of the solutions in the $C^{1} $ class is proved.