Condensation of the scalar field with Stuckelberg and Weyl Corrections in the background of a planar AdS-Schwarzschild black hole

Abstract

We study analytical properties of the Stuckelberg holographic superconductors with Weyl corrections. We obtain the minimum critical temperature as a function of the mass of the scalar field $m^2$. We show that in limit of the $m^2=-3$,$T_c^{Min}\approx 0.158047\sqrt[3]{\rho }$ which is close to the numerical estimate $T_c^{Numerical}\approx 0.170\sqrt[3]{\rho }$. Further we show that the mass of the scalar field in bounded from below by the $m^2>m_c^2$ where $m_c^2=-5.40417$. This lower bound is weaker and different from the previous lower bound $m^2=-3$ predicted by stability analysis. We show that in the Breitenlohner-Freedman bound, the critical temperature remains finite. Explicitly, we prove that here there is exist a linear relation between $<O_{\Delta }>$ and the chemical potential.

Matched with published version,Replaced to remove text overlaps with previous work by the same authors. arXiv admin note: substantial text overlap with arXiv:1106.0431

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