Integrable cases of gravitating static isothermal fluid spheres

Details Integrable cases of gravitating static isothermal fluid spheres Integrable cases of gravitating static isothermal fluid spheres

2001-07-17

arxiv.org/abs/gr-qc/0107060v1

J.Math.Phys. 43 (2002) 1029

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

13 pages, revtex

Scientific paper

10.1063/1.1431259

It is shown that different approaches towards the solution of the Einstein
equations for a static spherically symmetric perfect fluid with a gamma-law
equation of state lead to an Abel differential equation of the second kind. Its
only integrable cases at present are flat spacetime, de Sitter solution and its
Buchdahl transform, Einstein static universe and the Klein-Tolman solution.

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