Note on scalar fields non-minimally coupled to /(2+1)-gravity

Scalar fields nonminimally coupled to /(2+1)-gravity, in the presence of cosmological constant term, are considered. Nonminimal couplings are described by the term ζRΨ² 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 /ζ=0, and the Martínez-Zanelli black hole for /ζ=1/8. We obtain also two new solutions with nontrivial scalar field, for /ζ=1/6 and /ζ=1/8, respectively, nevertheless, the corresponding space-times can be reduced, via coordinate transformations, to the standard anti-de Sitter space.