Expanding spherically symmetric models without shear

S. D. Maharaj, P. G. L. Leach, R Maartens

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The integrability properties of the field equationL xx =F(x)L 2 of a spherically symmetric shear-free fluid are investigated. A first integral, subject to an integrability condition onF(x), is found, giving a new class of solutions which contains the solutions of Stephani and Srivastava as special cases. The integrability condition onF(x) is reduced to a quadrature which is expressible in terms of elliptic integrals in general. There are three classes of solution and in general the solution ofL xx =F(x)L 2 can only be written in parametric form. The case for whichF=F(x) can be explicitly given corresponds to the solution of Stephani. A Lie analysis ofL xx =F(x)L 2 is also performed. If a constant α vanishes, then the solutions of Kustaanheimo and Qvist and of this paper are regained. For α ≠ 0 we reduce the problem to a simpler, autonomous equation. The applicability of the Painlevé analysis is also briefly considered.
Original languageEnglish
Pages (from-to)35-50
JournalGeneral Relativity and Gravitation
Issue number1
Publication statusPublished - Jan 1996


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