2026/06/30 by Chao-Ming Zhang, Yun Soo Myung, Lina Zhang +2
#gr-qc
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 η 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 μ2eff sourced by the GB term. Unlike the asymptotically flat spacetime case, the onset of scalarization is not merely determined by μ2eff < 0, but it is constrained by the Breitenlohner-Freedman (BF) bound. In case that the BF bound is violated (η>2.25 with Λ=-0.5), one may find AdS-tachyonic instability. We find that for 0<η<2.25, the GB+ scalarization may be performed through spontaneous scalarization, while for η<0 the GB- scalarization is found to give the single branch of scalarized AdS black holes. For the GB+ scalarization in ηth≤η<2.25 with ηth 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^± scalarizations.