1979•Journal of Mathematical PhysicsRequires access

Petrov type N vacuum metrics and homothetic motions

W. D. Halford

Abstract

Petrov type N vacuum spaces which admit an expanding and/or twisting principal null congruence and a homothetic motion are considered. It is shown that there are no such spaces which admit two Killing vectors, or one Killing vector of special type. If there are no Killing vectors present, the form of the homothetic Killing vector is restricted to one possibility.

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Key concepts: Homothetic transformation, Killing vector field, Congruence (geometry), Type (biology), Mathematics, Pure mathematics, Motion (physics), Mathematical analysis