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The third Russian-Chinese conference on complex analysis, algebra, algebraic geometry and mathematical physics
May 12, 2016 15:50, Moscow, Steklov Mathematical Institute of RAS, Gubkina, 8
 


On homogeneous and isotropic universe

M. O. Katanaev

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

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M. O. Katanaev
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Abstract: We give a simple example of spacetime metric, illustrating that homogeneity and isotropy of space slices at all moments of time is not obligatory lifted to a full system of six Killing vector fields in spacetime, thus it cannot be interpreted as a symmetry of a four dimensional metric. The metric depends on two arbitrary and independent functions of time. One of these functions is the usual scale factor. The second function cannot be removed by coordinate transformations. We prove that it must be equal to zero, if the metric satisfies Einstein's equations and the matter energy momentum tensor is homogeneous and isotropic. A new, equivalent, definition of homogeneous and isotropic spacetime is given.

Language: English

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