Black holes with scalar hair: Extending from and beyond the Schwarzschild solution

We construct novel scalarized black hole (BH) solutions beyond the generalrelativity (GR) framework. These scalarized BH solutions are extended from theSchwarzschild one and the non-Schwarzschild one in the pure Einstein-Weylgravity. By studying the BH entropy and free energy, we demonstrate that thescalarized BH extending from the Schwarzschild one exhibits thermodynamicallypreferred. We obtain these novel solutions by directly solving the fullfourth-order equations of motion. This narrows the problematic solution spaceobtained by commonly adopted second-order reduction to physically valid spaces.Our findings also unveil the evasion of the no-hair theorem within the realm ofhigher-derivative gravity.