Revista mexicana de física
versión impresa 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.
Palabras llave : General relativity; conformal Killing vector field; Einstein equations.