Spontaneous Momentum Dissipation and Coexistence of Phases in Holographic Horndeski Theory

Understand

We discuss the possible phases dual to the AdS hairy black holes in Horndeski theory.

• In the probe limit breaking the translational invariance, we study the conductivity and we find a non-trivial structure indicating a collective excitation of the charge carriers as a competing effect of momentum dissipation and the coupling of the scalar field to Einstein tensor.
• Going beyond the probe limit, we investigate the spontaneous breaking of translational invariance near the critical temperature and discuss the stability of the theory.
• We consider the backreaction of the charged scalar field to the metric and we construct numerically the hairy black hole solution.