Properties of Schrödinger black holes from AdS space

Abstract

Properties of Schrödinger black holes are derived from those of AdS black holes expressed in light-cone coordinates with a particular normalization. Unlike the usual construction from an AdS black hole using a null Melvin twist, an AdS black hole in light-cone is simple and has a well-defined Brown-York procedure with the standard counterterms. Our procedure is demonstrated by the computation of the DC conductivity and the derivation of the R-charged black hole thermodynamic properties.

Holographic renormalization of Einstein-Maxwell-Dilaton theories

“…Here we briefly mention some examples of the finite boundary or counter terms in holography that have been discussed in the literature. One class of the examples that has introduced the finite counter term in holographic setup is in the context of R-charged black holes [60,61]. The black hole solutions have gauge fields and scalar fields.…”

“…In other wards, the first law of thermodynamics requires to have the counter term φ 2 , which is actually finite. Similarly, the thermodynamic properties of the R-charged black holes have been analyzed in the context of Schödinger space-time [61], where again the finite counter term proportional to φ 2 is required to satisfy the first law.…”

Holographic quantum criticality and strange metal transport

“…where the symbols g, R and are the determinant of the metric, the scalar curvature and the length scale of the theory related to the cosmological constant, respectively. We suppress the boundary terms needed for proper boundary conditions and renormalization, and consider the AdS-Schwartzschild black hole solution in light-cone coordinates [8,15]…”

“…The linear temperature dependence of the Ohmic resistivity was realized in spaces with AdS or Lifshitz scaling [41][42][43][44] and in the Schrödinger space [15,16]. Linear resistivity and a crossover to quadratic behavior were found in a larger class of scaling geometries in [43].…”

“…AdS space in the light-cone frame (ALCF) with z = 2 has also been put forward [13,14], as such a holographic background and a corresponding Schwarzschild black hole solution have been considered [8,15]. Notably, while the Schrödinger space and ALCF yield the same thermodynamic properties [7,8,10,15] and transport coefficients (when the latter are independent of an embedding scalar) [15,16], ALCF is simpler and has a well-defined holographic renormalization. 3 In this paper, we will analyze and report on the transport properties of ALCF, matching several universal experimental results of the normal state of cuprate superconductors at very low temperatures, which have been a subject of intensive research but remain largely unexplained over the last two decades.…”