  Darboux theorem in symplectic geometry is the crux of emergent gravity in
which the gravitational metric emerges from a noncommutative U(1)-theory.
Topological T-duality, on the other hand, is a relation between two a priori
different backgrounds (with different geometries, different fluxes and even
topologically distinct manifolds) which nevertheless behave identically from a
physical point of view. For us these backgrounds are principal torus bundles on
the same base manifold. In this article we review how these theories can be
naturally understood in the light of generalized geometry. Generalized geometry
provides an unifying framework for such a systematic approach and gives rise to
the group of Courant automorphism $Diff(M) \ltimes \Omega_{closed}^{2}(M)$ for
the $TM \oplus T^*M$ bundle. Here we propose a novel geometric construction for
the T-dual of an emergent gravity theory implemented between the
$\mathbb{T}$-bundles and this duality is realized using the
Gualtieri-Cavalcanti map that establishes an isomorphism between Courant
algebroids. In the case of flat spacetime we obtain that, under mild
assumptions, the T-dual of emergent gravity is again an emergent theory of
gravity. In the general case we obtained formulas for the T-dual of an emergent
metric in a $\mathbb{T}^2$-fibration, however due to the appearance of H-flux
after T-dualizing, the theory thus obtained can no longer be considered in the
usual framework of emergent gravity. This motivates the study of emergent
gravity with non trivial H-flux.
