Dynamics of radiation dominated branes: Vacuum dynamics from radiation

TL;DR

This paper reveals a symmetry in the equations governing spherically symmetric shells in 4- and 5-dimensional vacuum spacetimes, showing that radiation shells behave similarly to vacuum shells or domain walls.

Contribution

It identifies a symmetry between equations of state for polytropic fluids in the dynamics of shells in different dimensions, highlighting the equivalence for radiation shells and vacuum shells.

Findings

Radiation shells have the same equations of motion as vacuum shells.

Symmetry exists between polytropic fluid equations of state in 4D and 5D spacetimes.

The results unify the understanding of shell dynamics across different vacuum backgrounds.

Abstract

I point out a symmetry, between equations of state for polytropic fluids, in the equation of motion of a spherically symmetric singular shell embedded in 4-d and 5-d vacuum spacetimes. In particular the equation of motion of a shell consisting of radiation has the same form as for a vacuum shell or domain wall.