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Einstein Double Field Equations

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arxiv 1804.00964 v2 pith:OLSQRCH7 submitted 2018-04-03 hep-th gr-qcmath-phmath.MP

Einstein Double Field Equations

classification hep-th gr-qcmath-phmath.MP
keywords stringytensordoubleeinsteinenergy-momentumequationsfieldgeneral
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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Upon treating the whole closed string massless sector as stringy graviton fields, Double Field Theory may evolve into Stringy Gravity, i.e. the stringy augmentation of General Relativity. Equipped with an $\mathrm{O}(D,D)$ covariant differential geometry beyond Riemann, we spell out the definition of the Energy-Momentum tensor in Stringy Gravity and derive its on-shell conservation law from doubled general covariance. Equating it with the recently identified stringy Einstein curvature tensor, all the equations of motion of the closed string massless sector are unified into a single expression, $G_{AB}=8\pi G T_{AB}$, which we dub the `Einstein Double Field Equations'. As an example, we study the most general ${D=4}$ static, asymptotically flat, spherically symmetric, `regular' solution, sourced by the stringy Energy-Momentum tensor which is nontrivial only up to a finite radius from the center. Outside this radius, the solution matches the known vacuum geometry which has four constant parameters. We express these as volume integrals of the interior stringy Energy-Momentum tensor and discuss relevant energy conditions.

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