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Liouvillian integrability of gravitating static isothermal fluid spheres / Iacono, Roberto (ENEA-C. R. Casaccia(Italy)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We examine the integrability properties of the Einstein field equations for static, spherically symmetric fluid spheres, complemented with an isothermal equation of state, ρ = np. In this case, Einstein's equations can be reduced to a nonlinear, authonomous second order ODE for m/R (m is the mass inside the radius R) that has been solved analytically only for n = −1 and n = −3, yielding the cosmological solutions by De Sitter and Einstein, respectively, and for n = −5, case for which the solution can be derived from the De Sitter's one using a symmetry of Einstein's equations. [...]
2014 - DOI (Digital Object Identifier)

10.1063/1.4897213
Journal of Mathematical Physics, Vol. 55 (2014) , p. 102501

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