Peculiar anisotropic stationary spherically symmetric solution of Einstein equations

Abstract

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 nonvanishing spacelike components of the stressenergymomentum tensor. In spite of its strange nature, this solution has nontrivial descriptions of gravitational effects. We show that the main aspects found in the dark matter phenomena can be satisfactorily described by this geometry. We comment on the relevance it could have to consider nonvanishing spacelike components of the stressenergymomentum tensor ascribed to dark matter. © 2012 World Scientific Publishing Company.