Gravitational solitons (Q2747361)

A soliton is a solution of a nonlinear wave equation possessing the special property that the dispersion is just counterbalanced by nonlinear self-focussing. The result is a temporarily unchanged shape of the wave. The search for gravitational soliton solutions is the topic of the present monograph. Here, both the Einstein as well as the Einstein-Maxwell field equations are considered in great detail. One of the methods used goes back to one of the authors, Belinski, in collaboration with V. Zakharov, and is called ISM, the inverse scattering method.NEWLINENEWLINENEWLINEThe presented solutions include the following classes: Diagonal and nondiagonal forms of the cosmological solutions, including anisotropic and inhomogeneous solutions, Bianchi models, especially of types I and II. Then, cylindrically and axially symmetric space-times are considered, and several classes of colliding gravitational plane waves could be given in closed form.NEWLINENEWLINENEWLINEThe invariant geometric classification with Petrov types etc. of the considered space-times is also carefully deduced.