Hydrodynamics of RN AdS$_4$ black hole and Holographic Optics

TL;DR

This paper investigates the hydrodynamic behavior and optical properties of the RN AdS$_4$ black hole, revealing negative refraction at low frequencies and superconducting-like zero permeability in the dual field theory.

Contribution

It provides a detailed momentum-dependent hydrodynamic analysis and spectral function calculation for the RN AdS$_4$ black hole, extending holographic optics studies to this setting.

Findings

Negative index of refraction at low frequencies.

Zero permeability at static limit indicating superconductivity.

Spectral functions supporting holographic optical phenomena.

Abstract

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.\cite{amariti} for AdS$_5$. We also find that at static limit the medium has the zero permeability, a character of the superconductivity .