A perfect-fluid space-time of dimension n>3 with 1) irrotational velocity vector field, 2) null divergence of the Weyl tensor, is a generalised Robertson-Walker space-time with Einstein fiber. Condition 1) is verified whenever pressure and energy density are related by an equation of state. The contraction of the Weyl tensor with the velocity vector field is zero. Conversely, a generalized Robertson-Walker space-time with null divergence of the Weyl tensor is a perfect-fluid space-time.
A condition for a perfect-fluid space-time to be a generalised Robertson-Walker space-time / C.A. Mantica, L.G. Molinari, U.C. De. - In: JOURNAL OF MATHEMATICAL PHYSICS. - ISSN 0022-2488. - 57:2(2016), pp. 022508.1-022508.6.
A condition for a perfect-fluid space-time to be a generalised Robertson-Walker space-time
L.G. Molinari
;
2016
Abstract
A perfect-fluid space-time of dimension n>3 with 1) irrotational velocity vector field, 2) null divergence of the Weyl tensor, is a generalised Robertson-Walker space-time with Einstein fiber. Condition 1) is verified whenever pressure and energy density are related by an equation of state. The contraction of the Weyl tensor with the velocity vector field is zero. Conversely, a generalized Robertson-Walker space-time with null divergence of the Weyl tensor is a perfect-fluid space-time.
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