Holographic Superconductors in f(R) Gravity

Abstract

We study the holographic superconductors in f (R) gravity, and show how the critical temperature and condensate of the dual operators depend on the modifications of f (R) to Einstein gravity. A nontrivial planar black hole which is asymptotic to AdS spacetime is investigated for a specific f (R). The corrections to the thermal quantities of the black hole, the critical temperature and the condensate of the dual operator are all obtained in a perturbative approach explicitly. Some comments are given on the affections of such modifications to the holographic superconductors.

Higher-dimensional holographic superconductors in Born–Infeld electrodynamics and f(R) gravity

“…In this section, the specific model of f (R) gravity that we are going to study in this paper is introduced. We will follow some of the steps in [9,37,[64][65][66][67].…”

“…where M is the mass of the black hole. From now on, we will also take c 3 = 1 for simplicity, as was done in [37].…”

“…This higher-order theory predicts both earlytime inflation and late-time cosmic acceleration, and is also the only modified gravity theory that avoids the Ostrogradsky instability [56,57]. f (R) gravity is known to be Lorentz invariant, while higher-order curvature corrections appear in string theory as well, which makes f (R) gravity suitable for models using AdS/CFT [37,38,58]. Thus, f (R) gravity is an appropriate framework for the analysis of holographic superconductors.…”

“…These include superconductors in different dimensions [6][7][8][9], as well as a e-mail: alexandar.roussev@stud.uni-heidelberg.de (corresponding author) holographic superconductors in different backgrounds, e.g. in an external magnetic field [10][11][12][13][14][15], with Weyl corrections [16][17][18], in Horava-Lifshitz gravity [19][20][21][22], Gauss-Bonnet gravity [7,9,12,[23][24][25][26][27][28][29][30][31][32][33][34][35][36], and f (R) gravity [37,38]. Some studies also include non-linear electrodynamics [13,14,30,31,[38][39][40][41][42][43][44][45].…”

“…One common method in analyzing holographic superconductor models is the matching method [7,14,20,23,32,37,38]. The idea behind this analytic method is to take the solutions of the field equations near the horizon and the boundary and to match them at an intermediate point.…”