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Solitons and black hole in shift symmetric scalar-tensor gravity with cosmological constant. (English) Zbl 1395.83040
Summary: We demonstrate the existence of static, spherically symmetric globally regular, i.e. solitonic solutions of a shift-symmetric scalar-tensor gravity model with negative cosmological constant. The norm of the Noether current associated to the shift symmetry is finite in the full space-time. We also discuss the corresponding black hole solutions and demonstrate that the interplay between the scalar-tensor coupling and the cosmological constant leads to the existence of new branches of solutions. To linear order in the scalartensor coupling, the asymptotic space-time corresponds to an Anti-de Sitter 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/CFT correspondence. Finally, we demonstrate that – for physically relevant, small values of the scalar-tensor coupling – solutions with positive cosmological constant do not exist in our model.

MSC:
83C57 Black holes
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
83C15 Exact solutions to problems in general relativity and gravitational theory
35Q51 Soliton equations
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
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