Inhomogeneous Cosmological Models and Symmetry
Inhomogeneous cosmological models are studied extensively in the literature, in particular when the shear vanishes. The integrability properties of the field equation L xx = F(x)L2 of a spherically symmetric shear-free fluid are reviewed. A first integral, subject to an integrability condition on F(x), is found which generates a class of solutions which contains the solutions of Stephani (1983) and Srivastava (1987) as special cases. The integrability condition on F(x) is reduced to a quadrature. The Lie procedure for this equation is considered and we list various forms of F(x) and their Lie symmetry generators. A con- formal Killing vector in the t-r plane is assumed to exist and for this particular case the solution to the field equation is expressible in terms of Weierstrass elliptic functions.
KeywordsField Equation Conformal Symmetry Conformal Killing Einstein Field Equation Order Ordinary Differential Equation
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