Ayón-Beato, Eloy; García, Alberto; Macías, Alfredo; Pérez-Sánchez, José M. Note on scalar fields non-minimally coupled to \((2+1)\)-gravity. (English) Zbl 0983.83037 Phys. Lett., B 495, No. 1-2, 164-168 (2000). Summary: Scalar fields nonminimally coupled to \((2+1)\)-gravity, in the presence of cosmological constant term, are considered. Nonminimal 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 Martínez-Zanelli black hole for \(\zeta=1/8\). We obtain also two new solutions with nontrivial 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. Cited in 6 Documents MSC: 83C80 Analogues of general relativity in lower dimensions 81T20 Quantum field theory on curved space or space-time backgrounds Keywords:nonminimal couplings; anti-de Sitter space-time; Martínez-Zanelli black hole PDFBibTeX XMLCite \textit{E. Ayón-Beato} et al., Phys. Lett., B 495, No. 1--2, 164--168 (2000; Zbl 0983.83037) Full Text: DOI arXiv References: [1] Bergmann, P. G., Int. J. Theor. Phys., 1, 25 (1968) [2] Wagoner, R., Phys. Rev. D, 1, 3209 (1970) [3] Singh, T.; Rai, L. N., Gen. Rel. Grav., 15, 875 (1983) [4] Bekenstein, J. D., Ann. Phys. (NY), 82, 535 (1974) [5] Saa, A., Phys. Rev. D, 53, 7377 (1996) [6] Mayo, A. E.; Bekenstein, J. D., Phys. Rev. D, 54, 5059 (1996) [7] Bekenstein, J. D., (Dremin, I. M.; Semikhatov, A. M., Proceedings of Second Sakharov Conference in Physics, Moscow (1997), World Scientific: World Scientific Singapore), 761 [8] Chan, K. C.K., Phys. Rev. D, 55, 3564 (1997) [9] Chan, K. C.K.; Mann, R. B., Phys. Rev. D, 50, 2600 (1994) [10] Martı́nez, C.; Zanelli, J., Phys. Rev. D, 54, 3830 (1996) [11] Elsgoltz, L., Differential Equations and Variational Calculus (1977), MIR: MIR Moscow [12] Einsenhart, L. P., Riemannian Geometry (1925), Princeton Univ. Press: Princeton Univ. Press Princeton [13] Plebański, J., Conformal Equivalent Riemannian Spaces (1967), Monography CINVESTAV-IPN [14] Weinberg, S., Gravitation & Cosmology (1972), Wiley: Wiley New York [15] Garcı́a, A., Anti-de Sitter Black-Hole-like solutions and its dimensional reductions, (2000) [16] Bañados, M.; Teitelboim, C.; Zanelli, J., Phys. Rev. Lett., 69, 1849 (1992) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.