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The physical analysis of condensed matter systems can be difficult due tostrong coupling, but the mathematical context of the AdS/CFT correspondenceenables non-perturbative descriptions in terms of dual weakly coupled systems.This brief review explores the holographic condensed matter applications ofAdS/CFT, particularly through the lens of a high-$T_c$ superconductor outside aSchwarzchild black hole in Anti-de Sitter space. A simple two-dimensionalelectron condensate Lagrangian is examined first, as employed by G. T.Horowitz, later used to calculate a frequency-dependent conductivity and a freeenergy analysis; the asymptotics of both in this procedure, as examined by P.S\"aterskog, are also reviewed. An extended Lagrangian with a higher orderMaxwell term is assessed thereafter, with a conductivity peak obtained at lowfrequencies described well by the Drude model in certain limits. The behaviorof Drude model parameters in these limits is also investigated.

On the Behavior of Superconductors of High Critical Temperatures Outside Schwarzchild Black Holes in AdS Space