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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.

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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