Note on Scalar Fields Non-Minimally Coupled to (2+1)-Gravity

Abstract

Scalar fields non--minimally coupled to (2+1)-gravity, in the presence of cosmological constant term, are considered. Non-minimal couplings are described by the term $\zeta R{\Psi }^2$ in the Lagrangian. Within a class of static circularly symmetric space-times, it is shown that the only existing physically relevant solutions are the anti-de Sitter space-time for $\zeta =0$, and the Martinez-Zanelli black hole for $\zeta =1/8$. We obtain also two new solutions with non-trivial scalar field, for $\zeta =1/6$ and $\zeta =1/8$ respectively, nevertheless, the corresponding space-times can be reduced, via coordinate transformations, to the standard anti-de Sitter space.

5 pages, RevTex

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