Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2001-07-17
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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