$\mathbf{O}(D,D)$ completion of the Einstein Field Equations

Abstract: Upon treating the whole closed-string massless NS-NS sector as stringy graviton fields, Double Field Theory may evolve into Stringy Gravity'. In terms of an $\mathbf{O}(D,D)$ covariant differential geometry beyond Riemann, we present the definitions of the off-shell conserved stringy Einstein curvature tensor and the on-shell conserved stringy Energy-Momentum tensor. Equating them, all the equations of motion of the massless sector are unified into a single expression, $G_{AB}{=8\pi G} T_{AB}$, carrying $\mathbf{O}(D,D)$ vector indices, which we dubthe Einstein Double Field Equations'.