Noncommutative Differential Geometry via Deformation Quantization and Applications in Gravity

Noncommutative metrics and curvatures are discussed in frame of deformation quantization, and the noncommutative Einstein field equations are also proposed. The deformation of classical pp-wave is shown to be the exact solution of vacuum field equations and the deformation of classical Schwarzschild solution is shown to be the quantum black hole solution not depending on the time. Some physical implications of these solutions are also discussed. The talk is based on the joint works with Chaichian, Tureanu, W. Sun, D. Wang, N. Xie, R.B. Zhang.