(In)finite extent of stationary perfect fluids in Newtonian theory

Details (In)finite extent of stationary perfect fluids in Newtonian theory (In)finite extent of stationary perfect fluids in Newtonian theory

2011-08-24

arxiv.org/abs/1108.4791v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

17 pages, 1 figure

Scientific paper

For stationary, barotropic fluids in Newtonian gravity we give simple criteria on the equation of state and the "law of motion" which guarantee finite or infinite extent of the fluid region (irrespective of whether corresponding stationary solutions of the Newton-Euler system actually exist). Under more restrictive conditions, we can also exclude the presence of "hollow" configurations. Our main result, which does not assume axial symmetry, uses the virial theorem as key ingredient and generalizes a known result in the static case. In the axially symmetric case stronger results are obtained and examples are discussed.

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