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On reductions of Einstein equations

Krzysztof Rózga

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Abstract

A geometrical insight into the concept of reductions of Einstein equations is developed. A reduction of maximal rank is defined in terms of jet bundles. Some `classical' examples are examined in light of this definition. Then the simplest reductions are studied. These lead to the expansion-free radiation fields of Kundt. This provides a new point of view on this particular class of solutions of Einstein equations. It also offers another approach to the search for reductions of Einstein equations.

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What this paper is about

A geometrical insight into the concept of reductions of Einstein equations is developed. A reduction of maximal rank is defined in terms of jet bundles. Some `classical' examples are examined in light of this definition. Then the simplest reductions are studied. These lead to the expansion-free radiation fields of Kundt. This provides a new point of view on this particular class of solutions of Einstein equations. It also offers another approach to the search for reductions of Einstein equations.

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Available abstract

A geometrical insight into the concept of reductions of Einstein equations is developed. A reduction of maximal rank is defined in terms of jet bundles. Some `classical' examples are examined in light of this definition. Then the simplest reductions are studied. These lead to the expansion-free radiation fields of Kundt. This provides a new point of view on this particular class of solutions of Einstein equations. It also offers another approach to the search for reductions of Einstein equations.

Key concepts: Einstein, Physics, Einstein equations, Einstein's constant, Reduction (mathematics), Rank (graph theory), Einstein field equations, Point (geometry)

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