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

TL;DR

This paper finds new solitonic and black hole solutions in shift-symmetric scalar-tensor gravity with a negative cosmological constant, highlighting their potential relevance in AdS/CFT correspondence and the non-existence of similar solutions with positive cosmological constant.

Contribution

It introduces and analyzes the existence of static, spherically symmetric solitonic and black hole solutions in a shift-symmetric scalar-tensor gravity model with negative cosmological constant, including new solution branches.

Findings

Existence of regular solitonic solutions with negative cosmological constant.

Discovery of new black hole solution branches influenced by scalar-tensor coupling.

Solutions with positive cosmological constant do not exist for small coupling values.

Abstract

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 scalar-tensor 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.