A Structure Theorem for Stationary Perfect Fluids
Brendan Guilfoyle
TL;DR
This paper proves a structure theorem for stationary perfect fluids in relativity, showing they form a finite number of cells fibred by invariant surfaces, with special results for axially symmetric circular flows.
Contribution
It introduces a new structure theorem for stationary relativistic perfect fluids, detailing their fibred cell composition under mild physical assumptions.
Findings
Fluid consists of finitely many cells fibred by invariant annuli or tori
Axially symmetric circular flows are composed of rigidly rotating annuli or tori
Provides a mathematical classification of fluid structures in relativistic settings
Abstract
It is proven that, under mild physical assumptions, an isolated stationary relativistic perfect fluid consists of a finite number of cells fibred by invariant annuli or invariant tori. For axially symmetric circular flows it is shown that the fluid consists of cells fibred by rigidly rotating annuli or tori.
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