The Finite Temperatures Electron Star As A Holographic Non-feimi Liquid Model

Through the gauge-gravity dualities, string theory ofers powerful methods to studystrongly coupled field theories. In this dissertation, we will use this method to studyrelated topics in condensed matter physics. We study the following two distinct phenom-ena: superconductivity and non-Fermi liquids.In reference[1], Hartnoll and Tavanfar studied the zero temperature electron star asa holographic model for metallic criticalities. They found some interesting results: on theone hand, electron stars had an emergent Lifshitz scaling at low energies. They had aconjecture that this IR scaling region is a consequence of the two way interaction betweenemergent quantum critical bosonic modes and the finite density of fermions.Based on this model, we consider not only the electromagnetic, gravitational fieldand Interacting fermions with electricity, and that these charged particles satisfy finitetemperature thermodynamic distribution.If we added a condition that the approximationin which the fermion physics is determined by the local chemical potential, Einstein-Maxwell give the first law of the finite temperature thermodynamics.Numerical resultsshow that the model of charged particles Density distribution was shell structure.Finally,if we assume that the weak gravitational guess [2] is correct, then the absence of such ablack hole solution of equations.