Applying Phase Transitions in Scalar-Gauss-Bonnet Gravity to the AdS-CFT Correspondence

Some flavors of scalar-Gauss-Bonnet gravity admit both the Kerr solution and scalarized black holes. Scalarized black holes are characterized not only by a mass and spin, but also by a scalar charge. If coupled quadratically to the Gauss-Bonnet invariant, the scalar field forms bound states around the black hole below a critical black hole mass, which is set by the coupling constant. As a black hole grows beyond this critical mass, a phase transition occurs between the scalar charged and uncharged states. The AdS-CFT correspondence relates solutions in anti-de Sitter (AdS) spacetimes to a conformal field theory (CFT) on the boundary of that spacetime. For example, black holes in anti-de Sitter spacetimes correspond to thermal states of the CFT. Can scalarization happen in asymptotically AdS spacetimes, and does it describe a phase transition in the boundary field theory? Here, I demonstrate that scalar field bound state solutions can be found in arbitrary dimensions by analyzing perturbations of the Poincaré patch.