Notes on Emergent Gravity
arXiv:1206.0678 · doi:10.1007/JHEP09(2012)030
Abstract
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.
v3; 29 pages, minor clarifications for locally conformal symplectic structure and the origin of diffeomorphism, version to appear in JHEP