Narrow Results

We study the Lifshitz black hole in four dimensions with dynamical exponent z = 2 and we calculate analytically the quasinormal modes of scalar perturbations. These quasinormal modes allow to study the stability of the Lifshitz black hole and we have obtained that Lifshitz black hole is stable.

We analytically describe the properties of the s-wave holographic superconductor with the exponential nonlinear electrodynamics in the Lifshitz black hole background in four-dimensions. Employing an assumption the scalar and gauge fields backreact on the background geometry, we calculate the critical temperature as well as the condensation operator. Based on Sturm–Liouville method, we show that the critical temperature decreases with increasing exponential nonlinear electrodynamics and Lifshitz dynamical exponent, $z$, indicating that condensation becomes difficult. Also we find that the effects of backreaction has a more important role on the critical temperature and condensation operator in small values of Lifshitz dynamical exponent, while $z$ is around one. In addition, the properties of the upper critical magnetic field in Lifshitz black hole background using Sturm–Liouville approach is investigated to describe the phase diagram of the corresponding holographic superconductor in the probe limit. We observe that the critical magnetic field decreases with increasing Lifshitz dynamical exponent, $z$, and it goes to zero at critical temperature, independent of the Lifshitz dynamical exponent, $z$.