Abstract:
We present the analytic Lifshitz solutions for a scalar field model non minimally coupled
with the abelian gauge field in N dimensions. We also consider the presence of cosmological
constant . The Lifshitz parameter z appearing in the solution plays the role of the Lorentz
breaking parameter of the model. We investigate the thermodynamical properties of the
solutions and discuss the energy issue. Furthermore, we study the hairy black hole solutions
in which the abelian gauge field breaks the symmetry near the horizon. In the holographic
picture, it is equivalent to a second order phase transition. Explicitly we show that there exist
a critical temperature which is a function of the Lifshitz parameter z. The system below the
critical temperature becomes superconductor, but the critical exponent of the model remains
the same of the usual holographic superconductors without the higher order gravitational
corrections, in agreement with Gainsbourg-Landau theories.
