Dinamic model of spherical perturbations in Friedmann Universe

TL;DR

This paper develops a comprehensive dynamic model for spherical perturbations in Friedmann universes, deriving exact solutions for their evolution with arbitrary equations of state, including singular mass sources.

Contribution

It introduces a self-consistent system of equations for linear spherically symmetric perturbations with exact solutions for arbitrary equations of state.

Findings

Derived an evolutionary equation for the mass of particle-like sources.

Obtained exact solutions for perturbations with arbitrary equations of state.

Extracted the singular part of perturbations related to massive sources.

Abstract

A selfconsistent system of equations describing evolution of linear spherically symmetric perturbations in Fridmann world by an arbitrary equation of state is obtained. The perturbations singular part corresponding to massive particle-like source is extracted, an evolutionary equation for mass of this source is obtained and exactly solved. An exact solution of evolutionary equations of state for perturbations by an arbitrary equation of state is constructed.