Gravitational collapse in the expanding Universe

TL;DR

This paper investigates gravitational collapse in an expanding universe using the Tolman metric, deriving a formula for the maximum galaxy radius based on mass and the Hubble parameter.

Contribution

It introduces a novel analytical approach linking gravitational collapse dynamics with cosmological expansion parameters.

Findings

Maximum galaxy radius formula: (GM/H^2)^{1/3}

Collapse behavior influenced by the cosmological constant

Analytical model for pressureless fluid collapse in expanding spacetime

Abstract

We use the Tolman metric to describe gravitational collapse of a sphere of a fluid without pressure in spacetime with the Hubble parameter $H$ related to the cosmological constant. We show that the largest radius of a galaxy formed from such a fluid with mass $M$ is given by $(GM/H^2)^{1/3}$.