Evolution of Thick Walls in Curved Spacetimes

TL;DR

This paper extends the formalism for thick shells in curved spacetimes to include arbitrary velocities and thicknesses, deriving equations of motion for spherically symmetric dust shells in various cosmological backgrounds.

Contribution

It introduces a generalized formalism for thick walls with arbitrary properties and derives their equations of motion in different curved spacetime settings.

Findings

Derived equations of motion for thick shells in vacuum and FRW spacetimes.

Extended previous formalism to include arbitrary velocities and thicknesses.

Applicable to spherically symmetric dust shells in cosmological models.

Abstract

We generalize our previous thick shell formalism to incorporate any codimension-1 thick wall with a peculiar velocity and proper thickness bounded by arbitrary spacetimes. Within this new formulation we obtain the equation of motion of a spherically symmetric dust thick shell immersed in vacuum as well as in Friedmann-Robertson-Walker spacetimes.