On the stability of spherically symmetric and wormhole solutions supported by the sine-Gordon ghost scalar field

In this paper we investigate wormhole and spherically symmetric solutions in 4D gravity plus a matter source consisting of a ghost scalar field with a sine-Gordon potential. For the wormhole solutions we also include the possibility of electric and/or magnetic charges. For both types of solutions we perform a linear stability analysis and show that the wormhole solutions are stable and that when one turns on the electric and/or magnetic field the solution remains stable. The linear stability analysis of the spherically symmetric solutions indicates that they can be stable or unstable depending on one of the parameters of the system. This result for the spherically symmetric solution is nontrivial since a previous investigation of 4D gravity plus a ghost scalar field with a $\lambda \phi ^4$ interaction found only unstable spherically symmetric solutions. Both the wormhole and spherically symmetric solutions presented here asymptotically go to anti-de-Sitter space-time.