  Emergent gravity is aimed at constructing a Riemannian geometry from U(1)
gauge fields on a noncommutative spacetime. But this construction can be
inverted to find corresponding U(1) gauge fields on a (generalized) Poisson
manifold given a Riemannian metric (M, g). We examine this bottom-up approach
with the LeBrun metric which is the most general scalar-flat Kahler metric with
a U(1) isometry and contains the Gibbons-Hawking metric, the real heaven as
well as the multi-blown up Burns metric which is a scalar-flat Kahler metric on
C^2 with n points blown up. The bottom-up approach clarifies some important
issues in emergent gravity.
