On the stability of exceptional Brans–Dicke wormholes

In our previous papers we have analyzed the stability of vacuum and electrovacuum static, spherically symmetric space-times in the framework of the Bergmann–Wagoner–Nordtvedt class of scalar-tensor theories (STT) of gravity. In the present paper, we continue this study by examining the stability of exceptional solutions of the Brans–Dicke theory with the coupling constant ω =0 ω = 0 that were not covered in the previous studies. Such solutions describe neutral or charged wormholes and involve a conformal continuation: the standard conformal transformation maps the whole Einstein-frame manifold ME M E to only a part of the Jordan-frame manifold MJ M J , which has to be continued beyond the emerging regular boundary S, and the new region maps to another manifold ME M E ₋ - . The metric in MJ M J is symmetric with respect to S only if the charge q is zero. Our stability study concerns radial (monopole) perturbations, and it is shown that the wormhole is stable if q ≠ 0 q ≠ 0 and unstable only in the symmetric case $$q=0$$ q = 0 .