Conformal structure of a Schwarzschild black hole immersed in a Friedman universe (original) (raw)
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Addentum to: Conformal Invariance and Near-extreme Rotating AdS Black Holes
We obtained retarded Green's functions for massless scalar fields in the background of near-extreme, near-horizon rotating charged black hole of five-dimensional minimal gauged supergravity in Phys. Rev. D84, 044018 (2011). For general nonextreme black holes, we also derived the radial part of the massless Klein-Gordon equation with zero azimuthal-angle eigenvalues, and showed that it is a general Heun's equation with a regular singularity at each horizon uk (k=1,2,3) and at infinity. We derived explicitly that the residuum of a pole at each uk is associated with the surface gravity there. In this addendum, probing regular singularities at each uk we complete the derivation of the full radial equation with nonzero azimuthal-angle eigenvalues. The residua now include modifications by the angular velocities at respective horizons. This result completes the analysis of the wave equation for the massless Klein-Gordon equation for the general rotating charged black hole of five-dimensional minimal gauged supergravity.
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Hidden and Generalized Conformal Symmetry of Kerr-Sen Spacetimes
It is recently conjectured that generic non-extremal Kerr black hole could be holographically dual to a hidden conformal field theory in two dimensions. Moreover, it is known that there are two CFT duals (pictures) to describe the charged rotating black holes which correspond to angular momentum J and electric charge Q of the black hole. Furthermore these two pictures can be incorporated by the CFT duals (general picture) that are generated by SL(2,Z) modular group. The general conformal structure can be revealed by looking at charged scalar wave equation in some appropriate values of frequency and charge. In this regard, we consider the wave equation of a charged massless scalar field in background of Kerr-Sen black hole and show in the "near region", the wave equation can be reproduced by the Casimir operator of a local SL(2,R)L×SL(2,R)R hidden conformal symmetry. 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)L×SL(2,R)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.
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Deformed Hidden Conformal Symmetry for Rotating Black Holes
The generic non-extremal Kerr-Newman black holes are holographically dual to hidden conformal field theories in two different pictures. The two pictures can be merged together to the CFT duals in general picture that are generated by SL(2,Z) modular group. We find some extensions of the conformal symmetry generators that yield an extended local family of SL(2,R)L×SL(2,R)R hidden conformal symmetries for the Kerr-Newman black holes parameterized by one deformation parameter. The family of deformed hidden conformal symmetry for Kerr-Newman black holes also provides a set of deformed hidden conformal generators for the charged Reissner-Nordstrom black holes. The set of deformed hidden conformal generators reduce to the hidden SL(2,R) conformal generators for the Reissner-Nordstrom black hole for specific value of deformation parameter. We also find agreement between the macroscopic and microscopic entropy and absorption cross section of scalars for the Kerr-Newman black hole by considering the appropriate temperatures and central charges for the deformed CFTs.
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