Superconducting and Anti-Ferromagnetic Phases of Spacetime

A correspondence between the $SO(5)$ theory of High-T${}_C$ superconductivity and antiferromagnetism, put forward by Zhang and collaborators, and a theory of gravity arising from symmetry breaking of a $SO(5)$ gauge field is presented. A physical correspondence between the order parameters of the unified SC/AF theory and the generators of the gravitational gauge connection is conjectured. A preliminary identification of regions of geometry, in solutions of Einstein's equations describing charged-rotating black holes embedded in deSitter spacetime, with SC and AF phases is carried out.