Ruíz Ruíz, FernandoOrtiz, Miguel E.Gibbons, Gary W.2023-06-202023-06-201989-03-151 A. Vilenkin, Phys. Rep. 121, 263 (1985). 2 H. B.Nielsen and P. Olesen, Nucl. Phys. B61,45 (1973). 3 D. Garfinkle, Phys. Rev. D 32, 1323 (1985). 4 P. Laguna-Castillo and R. Matzner, Phys. Rev. D 36, 3663 (1987). 5 R. Gregory, Phys. Rev. Lett. 59, 740 (1987). 6 G. H. Derrick, J. Math. Phys. 5, 1252 (1964). 7 K. Thorne, Phys. Rev. 138, B251 (1965). 8 D. Harari and P. Sikivie, Phys. Rev. D 37, 3448 (1988). 9 D. Kramer, H. Stephani, M. MacCallum, and E. Herlt, Exact Solutions of Einstein's Field Equations (VEB Deutscher Verlag der Wissenschaften, Berlin, 1980). 10 C. W. Misner, Phys. Rev. D 18, 4510 (1978). 11 A. Comtet and G. W. Gibbons, Nucl. Phys. B299, 719 1988). 12 M. Gell-Mann and B.Zwiebach, Phys. Lett. 147B, 111 (1984). 13 R. Gregory, Phys. Lett. B 215, 663 (1988). 14 A. D. Cohen and D. B.Kaplan, Phys. Lett. B 215, 67 (1988)0556-282110.1103/PhysRevD.39.1546https://hdl.handle.net/20.500.14352/59049© 1989 The American Physical Society We would like to thank Tanmay Vachaspati and Ruth Gregory for valuable discussions. F.R.R. is indebted to the Department of Applied Mathematics and Theoretical Physics for their kind hospitality in Cambridge and to the Spanish Ministry of Education and Science for support.We consider σ-model strings and U(1) global strings coupled to gravity and look for static solutions with whole cylinder symmetry. We prove that in both cases there are no regular spatially compact solutions. The U(1) global string admits no asymptotically well-behaved solutions, whereas cr model strings can be constructed under certain assumptions. Finally we present somesingular solutions and show that one of the corresponds to a physical global string.engjournal articlehttp://dx.doi.org/10.1103/PhysRevD.39.1546http://journals.aps.orgopen access53Astronomy & AstrophysicsPhysicsParticles & FieldsFísica (Física)22 Física