Curvature-induced scalarization of charged AdS black holes

Abstract

We investigate how a negative cosmological constant affects the Gauss-Bonnet (GB) scalarization in the Einstein-Maxwell-scalar-Gauss-Bonnet theory with a scalar coupling constant $\eta$ to GB term. We focus on the instability of Reissner-Nordström-AdS (RN-AdS) black holes under a scalar perturbation governed by an effective mass ${\mu }_{\text{eff}}^2$ sourced by the GB term. Unlike the asymptotically flat spacetime case, the onset of scalarization is not merely determined by ${\mu }_{\text{eff}}^2<0$, but it is constrained by the Breitenlohner-Freedman (BF) bound. In case that the BF bound is violated ($\eta >2.25$ with $\Lambda =-0.5$), one may find AdS-tachyonic instability. We find that for $0<\eta <2.25$, the GB${}^{+}$ scalarization may be performed through spontaneous scalarization, while for $\eta <0$ the GB${}^{-}$ scalarization is found to give the single branch of scalarized AdS black holes. For the GB${}^{+}$ scalarization in ${\eta }_{th}\le \eta <2.25$ with ${\eta }_{th}$ threshold instability, we obtain the single branch ($n=0$ fundamental branch) of scalarized AdS black holes, in contrast to the infinite branches in asymptotically flat spacetime. A bulk fixed-charge thermodynamic analysis is performed thoroughly for GB${}^{\pm }$ scalarizations.

32 pages, 12 figures