Soliton solutions of the Einstein equations generated from cosmological solutions with additional symmetry

R. T. Jantzen
1980 Il Nuovo Cimento B Series 11  
rieevuto il 28 Luglio 1980) Snmmary. --A classification of inequivalent Belinsky-Zakharov coordinate systems is given for all spatially homogeneous and spatially self-similar vacuum and stiff perfect-fluid space-times which admit a 2-dimensional Abelian group of isometrics acting orthogonally transitively on 2-dimensional spacelike surfaces, the sytnmetry which is necessary for the application of the Belinsky-Zakharov solution-generating technique. The Bctinsky-Zakharov complex matrix function
more » ... is then found for all known co-ordinate systems in which the component matrix of the space-time metric is diagonal. Using only algebraic manipulations involving the v-matrix, one can in principle generate new exact (inhomogeneous) cosmological solutions containing an arbitrary number of (~ solitons >~. -Introduction. BELII~SKu and ZAKT~A~OV (I,~) have developed a technique for generating new vacuum (or stiff perfect fluid) solutions of the Einstein equations from existing solutions, for the case of space-times on which a 2-dimensionalAbeli~n isometry group G~ acts orthogonally transitively (3) on 2-dimensional spacelike orbits. (The timelike ease will not be considered here.) For such spacetimes, co-ordinates adapted to the action of the symmetry group may be chosen (1) V. 2~k. ]:~]~LINSKY and V. E. ZAKHA~OV: Soy. Phys. JETP, 48, 985 (1978). (2) V.A.
doi:10.1007/bf02721316 fatcat:jiiuoxkkvrccne674yaiqypexi