  We consider d-dimensional Riemanian manifolds which admit d-2 commuting
space-like Killing vector fields, orthogonal to a surface, containing two
one-parametric families of light-like curves. The condition of the Ricci tensor
to be zero gives Ernst equations for the metric. We write explicitly a family
of local solutions of this equations corresponding to arbitrary initial data on
two characteristics in terms of a series. These metrics describe scattering of
2 gravitational waves, and thus we expect they are very interesting. Ernst
equations can be written as equations of motion for some 2D Lagrangian, which
governs fluctuations of the metric, constant in the Killing directions. This
Lagrangian looks essentially as a 2D chiral field model, and thus is possibly
treatable in the quantum case by standart methods. It is conceivable that it
may describe physics of some specially arranged scattering experiment, thus
giving an insight for 4D gravity, not treatable by standart quantum field
theory methods. The renormalization flow for our Lagrangian is different from
the flow for the unitary chiral field model, the difference is essentially due
to the fact that here the field is taking values in a non-compact space of
symmetric matrices. We investigate the model and derive the renormalized action
in one loop.
