Chinea Trujillo, Francisco Javier2023-06-212023-06-2119831. F. J. Ernst, Phys. Bev. 167, 1175 (1968). 2. D. Kramer and G. Neugebauer, Commun. Math. Phys. 10, 132 (1968). 3. R. Geroch, J. Math. Phys. (N.Y.) 13, 394 (1972). 4. W. Kinnersley, J. Math. Phys. (N.Y.) 18, 1529 (1977). 5. W. Kinnersley and D. M. Chitre, Phys. Bev. Lett. 4O, 1608 (1978). 6. D. Maison, Phys. Bev. Lett. 41, 521 (1978), and J. Math. Phys. (N.Y.) 20, 871 (1979). 7. C. Hoenselaers, W. Kinnersley, and B. C. Xanthopoulos, Phys. Bev. Lett. 42, 481 (1978), and J. Math. Phys. (N.Y.) 20, 2530 (1979). 8. V. A. Belinskii and V. E. Zakharov, Zh. Eksp. Teor. Fiz. 75, 1955 (1978) [ Sov. Phys. JETP 48, 985 (1978)]. 8. Backlund transformations for the Ernst equation of general relativity were independently introduced for the first time in the following: B. K. Harrison, Phys. Bev. Lett. 41, 1197, 1835(E) (1978); G. Neugebauer, J. Phys. A12, L67 (1979). Other expressions for Bäcklund transformations of the same problem, and their relation with gauge transformations, may be seen in the followirg: M. Omote and M. Wadati, J. Math. Phys. (N.Y.) 22, 961 (1981); F.J. Chinea, Phys. Bev. D 24, 1053 (1981), and 26, 2175(E) (1982), and Physica (Utrecht) 114A, 151 (1982). 10. T. Lewis, Proc. Boy. Soc. London, Ser. A 136, 176 (1932); A. Papapetrou, Ann. Phys. (Leipzig) 12, 309 (1953). 11. G. Neugebauer and D. Kramer, Exp. Tech. Phys. 28, 3 (1980); G. Neugebauer, J. Phys. A 13, L19 (1980); D. Kramer and G. Neugebauer, Phys. Lett. 75A, 259 (1980). 12. B. K. Harrison, Phys. Bev. D 21, 1695 (1980). 13. K. Pohlmeyer, Commun. Math. Phys. 46, 207 (1976). 14. A permutability property for Bäcklund transformations of the Ernst equation was found by G. Neugebauer (Ref. 9)0031-900710.1103/PhysRevLett.50.221https://hdl.handle.net/20.500.14352/64979©1983 The American Physical Society. Financial support by Comision Asesora de Investigacion Científica y Técnica is gratefully acknowledged.Vector Bäcklund transformations which relate solutions of the vacuum Einstein equations having two commuting Killing fields are introduced. Such transformations generalize those found by Pohlmeyer in connection with the nonlinear δ model. A simple algebraic superposition principle, which permits the combination of Bäcklund transforms in order to get new solutions, is given. The superposition preserves the asymptotic flatness condition, and the whole scheme is manisfestly O(2, 1) invariant.engjournal articlehttp://dx.doi.org/10.1103/PhysRevLett.50.221http://journals.aps.orgopen access51-73PhysicsMultidisciplinaryFísica-Modelos matemáticosFísica matemática