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Holographic description of three dimensional Godel black hole

Three dimensional Gödel black hole is a solution to Einstein-Maxwell-Chern-Simons theory with a negative cosmological constant. We have studied the hidden conformal symmetry for massive scalar field without any additional condition in the background of three dimensional non-extremal and extremal Gödel black holes. This conformal symmetry is uncovered by the observation that the radial wave equations in both cases can all be rewritten in the form of $SL(2, R)$ Casimir operators through introducing two sets of conformal coordinates to write the $SL(2, R)$ generators. At last, we give the holographic dual descriptions of Bekenstein-Hawking entropies of non-extremal and extremal black holes from Cardy formula of conformal field theory.