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Hydrodynamics of RN AdS$${}_{4}$$ black hole and holographic optics. (English) Zbl 1301.81213
Summary: We consider the AdS$${}_{4}$$ RN black hole and work out the momentum dependent hydrodynamic analysis for the vector modes. We also perform the spectral function calculation of the dual field theory. As an application, we consider the permittivity and permeability and find that for low frequency regime, the index of refraction is found to be negative, supporting the claim made in ref. [A. Amariti et al., ibid. 2011, No. 4, Paper No. 036 (2011), arXiv:1006.5714] for AdS$${}_{5}$$.

##### MSC:
 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 83C57 Black holes 81T13 Yang-Mills and other gauge theories in quantum field theory 81V17 Gravitational interaction in quantum theory 81T20 Quantum field theory on curved space or space-time backgrounds 81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics 82D15 Statistical mechanics of liquids 83F05 Relativistic cosmology
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