Spontaneous Holographic Scalarization of Black Holes in Einstein-Scalar-Gauss-Bonnet Theories.

We holographically investigate the scalarization in the Einstein-Scalar-Gauss-Bonnet gravity with a negative cosmological constant. We find that instability exists for both Schwarzschild-AdS and Reissner-Nordstrom-AdS black holes with planar horizons when we have proper interactions between the scalar field and the Gauss-Bonnet curvature corrections. We relate such instability to possible holographic scalarization and construct the corresponding hairy black hole solutions in the presence of the cosmological constant. Employing the holographic principle we expect that such bulk scalarization corresponds to the boundary description of the scalar hair condensation without breaking any symmetry, and we calculate the related holographic entanglement entropy of the system. Moreover, we compare the mechanisms of the holographic scalarizations caused by the effect of the coupling of the scalar field to the Gauss-Bonnet term and holographic superconductor effect in the presence of an electromagnetic field, and unveil their differences in the effective mass of the scalar field, the temperature dependent property and the optical conductivity.