Scalarization of Taub-NUT black holes in extended scalar-tensor-Gauss-Bonnet theory

A bstract Recently, the scalarization of the Schwarzschild black hole has been extensively studied. In this work, we explore the scalarization of the Taub-NUT black hole within the context of the extended scalar-tensor-Gauss-Bonnet theory, which admits a Ricci-flat Taub-NUT black hole as a solution. We carried out an analysis of the probe scalar field to identify the mass parameter and NUT parameter ( m , n ) where hairy black holes begin to emerge. Subsequently, we used the shooting method to construct the scalarized Taub-NUT black hole numerically. Unlike the Schwarzschild case, there are two branches of new hairy black holes that are smoothly connected. We calculated the entropy of the scalarized black holes and compared these entropies with those of scalar-free Taub-NUT black holes, finding that the entropies of the new hairy black holes are larger. A novel phenomenon emerges in this system: the entropy of the black holes at the bifurcation point is constant for a positive mass parameter. We then conjecture a maximal entropy bound for all scalarized black holes whose mass parameter at the bifurcation point is greater than zero.