The Lemaitre Model and the Generalisation of the Cosmic Mass

TL;DR

This paper revisits the Lemaitre metric with pressure, providing a calculational framework to analyze cosmic mass and apparent horizons, revealing pressure complicates invariant mass definitions but preserves horizon relations.

Contribution

It introduces a calculational algorithm for the Lemaitre metric with pressure and analyzes its implications for mass and horizon relations in cosmology.

Findings

Pressure complicates invariant mass separation.

Apparent horizon relation remains unchanged with pressure.

Mass definition challenges in the Lemaitre model.

Abstract

We consider the spherically symmetric metric with a comoving perfect fluid and non-zero pressure -- the Lemaitre metric -- and present it in the form of a calculational algorithm. We use it to review the definition of mass, and to look at the apparent horizon relations on the observer's past null cone. We show that the introduction of pressure makes it difficult to separate the mass from other physical parameters in an invariant way. Under the usual mass definition, the apparent horizon relation, that relates the diameter distance to the cosmic mass, remains the same as in the Lemaitre-Tolman case.