Deformed Hidden Conformal Groups for Rotating Black Holes

Abstract

The general non-extremal Kerr black hole is holographically dual to a conformal field theory in two dimensions. It is known that two CFT duals or pictures, can describe the charged rotating black holes. They correspond respectively to the angular momentum J and the electric charge Q of the black hole. Moreover, these two pictures can be incorporated by a CFT dual or general picture, which is generated by an SL(2, Z) modular group. To construct the general conformal structure, one can look at the charged scalar wave equation, in some appropriate values of frequency and charge. We consider the wave equation of a charged massless scalar field in the background of Kerr-Sen black hole and show, the wave equation can be reproduced by the Casimir operator of a local SL(2, R) × SL(2, R) hidden conformal symmetry, in the near region limit. We can find the exact agreement between macroscopic and microscopic physical quantities like entropy and absorption cross section of scalars for Kerr-Sen black hole. We then find an extension of vector fields that in turn yields an extended local family of SL(2, R) × SL(2, R) hidden conformal symmetries, parameterized by one parameter. For some special values of the parameter, we find a copy of SL(2, R) hidden conformal algebra for the charged Gibbons-Maeda-Garfinkle-Horowitz-Strominger black hole in the strong deflection limit. This proceedings article is entirely based on the results in the published paper [1].