Approximate Symmetries in General Relativity

Roustam Zalaletdinov

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Approximate Symmetries in General Relativity

Roustam Zalaletdinov

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Abstract

The problem of finding an appropriate geometrical/physical index for measuring a degree of inhomogeneity for a given space-time manifold is posed. Interrelations with the problem of understanding the gravitational/informational entropy are pointed out. An approach based on the notion of approximate symmetry is proposed. A number of related results on definitions of approximate symmetries known from literature are briefly reviewed with emphasis on their geometrical/physical content. A definition of a Killing-like symmetry is given and a classification theorem for all possible averaged space-times acquiring Killing-like symmetries upon averaging out a space-time with a homothetic Killing symmetry is proved.

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Roustam Zalaletdinov. 1999-12-07. Approximate Symmetries in General Relativity. https://arxiv.org/abs/gr-qc/9912021

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