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

Understand

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.