Holographic superconductor in the exact hairy black hole

Understand

We study the charged black hole of hyperbolic horizon with scalar hair (charged Martinez-Troncoso-Zanelli: CMTZ black hole) as a model of analytic hairy black hole for holographic superconductor.

• For this purpose, we investigate the second order phase transition between CMTZ and hyperbolic Reissner-Nordstr\"om-AdS (HRNAdS) black holes.
• However, this transition unlikely occur.
• As an analytic treatment for holographic superconductor, we develop superconductor in the bulk and superfluidity on the boundary using the CMTZ black hole below the critical temperature.