Dynamics of radiation dominated branes: Vacuum dynamics from radiation

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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.
12 pages, 1 fig., typos and reference corrected. Submitted for publication

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