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Revista mexicana de física

Print version ISSN 0035-001X

Abstract

ESTEVEZ-DELGADO, J  and  ZANNIAS, T. From conformal Killing vector fields to boost-rotational symmetry. Rev. mex. fis. [online]. 2007, vol.53, suppl.2, pp.41-49. ISSN 0035-001X.

We discuss a connection between three-dimensional Riemannian manifolds (Σ,) admitting a special conformal Killing vector field ξ and static vacuum or non-vacuum spacetimes. Any such (Σ,) generates a vacuum spacetime (M,g) but it also generates a spacetime (M, g, Φ), where (g, Φ) satisfies the Einstein-Klein-Gordon massless minimally coupled gravity equations, or the Einstein-Conformal scalar field equations. The resulting spacetimes either admit four Killing vector fields or possess boost and rotational symmetry. We argue that this connection goes beyond the vacuum or Einstein-scalar field system and it should be viewed as a mechanism of generating solutions for the Einstein equations, admitting a hypersurface orthogonal Killing vector field.

Keywords : General relativity; conformal Killing vector field; Einstein equations.

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