One also requires that these two metrics satisfy a transversality (or "orthogonality") condition, h a b t b c = 0 {\displaystyle h^{ab}t_{bc}=0} . Thus, one defines a classical spacetime as an ordered quadruple ( M , t a b , h a b , ∇ ) {\displaystyle (M,t_{ab},h^{ab},\nabla )} , where t a b {\displaystyle t_{ab}} and h a b {\displaystyle h^{ab}} are as described, ∇ {\displaystyle \nabla } is a metrics-compatible covariant derivative operator; and the metrics satisfy the orthogonality condition. One might say that a classical spacetime is the analog of a relativistic spacetime ( M , g a b ) {\displaystyle (M,g_{ab})} , where g a b {\displaystyle g_{ab}} is a smooth Lorentzian metric on the manifold M {\displaystyle M} .