  Motivated by studies on gravitational lenses, we present an exact solution of
the field equations of general relativity, which is static and spherically
symmetric, has no mass but has a non-vanishing spacelike components of the
stress-energy-momentum tensor. In spite of its strange nature, this solution
provides with non-trivial descriptions of gravitational effects. We show that
the main aspects found in the \emph{dark matter phenomena} can be
satisfactorily described by this geometry. We comment on the relevance it could
have to consider non-vanishing spacelike components of the
stress-energy-momentum tensor ascribed to dark matter.
