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We demonstrate the existence of static, spherically symmetric globallyregular, i.e. solitonic solutions of a shift-symmetric scalar-tensor gravitymodel with negative cosmological constant. The norm of the Noether currentassociated to the shift symmetry is finite in the full space-time. We alsodiscuss the corresponding black hole solutions and demonstrate that theinterplay between the scalar-tensor coupling and the cosmological constantleads to the existence of new branches of solutions. To linear order in thescalar-tensor coupling, the asymptotic space-time corresponds to an Anti-deSitter space-time with a non-trivial scalar field on its conformal boundary.This allows the interpretation of our solutions in the context of the AdS/CFTcorrespondence. Finally, we demonstrate that - for physically relevant, smallvalues of the scalar-tensor coupling - solutions with positive cosmologicalconstant do not exist in our model.

Solitons and black hole in shift symmetric scalar-tensor gravity with cosmological constant