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arXiv 1206.0678hep-thgr-qcmath-phmath.MP
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关于突现引力的注记

Notes on Emergent Gravity

Sunggeun Lee, Raju Roychowdhury, Hyun Seok Yang

摘要:

突现引力的目标是在非对易时空中由U(1)规范场构造黎曼几何。但是这个构造可以反过来在给定黎曼度量(M,g)的(广义)泊松流形上找到相应的U(1)规范场。我们用LeBrun度量来检验这种自底向上的方法,LeBrun度量是最一般的具有U(1)等距的标量平坦的Kahler度量,包含Gibbons-Hawking度量、真正的天堂以及多重爆破的Burns度量,Burns度量是C^2上具有n个爆破点的标量平坦的Kahler度量。自下而上的方法澄清了涌现引力中的一些重要问题。

英文摘要:

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.

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