MG15 - Talk detail

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The holography for rotating black holes provides a description of black hole physics in terms of a certain two-dimensional conformal field theory (CFT). The first realization of the holography for rotating black holes was proposed for extremal Kerr black hole. The proposal states that the near horizon geometry of the extremal Kerr black hole does have a dual holographic description in terms of a two-dimensional chiral CFT. The proposal has been studied and extended extensively for other extremal or near extremal rotating black holes. For all extremal and near-extremal black holes in different dimensions, the physical quantities associated to black hole (such as the entropy or scattering cross section) are in agreement with the corresponding microscopic dual quantities in CFT. In this talk, we find the explicit form of two-point function for the conformal spin-2 energy momentum operators on the near horizon of a near extremal Kerr black hole by variation of a proper boundary action. In this regard, we consider an appropriate boundary action for the gravitational perturbation of the Kerr black hole. We consider the boundary action and calculate it on-shell to find the two-point functions for the spin-2 energy momentum tensor fields, on the near horizon region of the Kerr black hole. We show that the variation of the boundary action with respect to the boundary fields yields the two-point function for the energy momentum tensor of a conformal field theory. We find agreement between the two-point function and the correlators of the dual conformal field theory to the Kerr black hole.

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