

The third RussianChinese 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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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

