Extended black holes in strong gravitational waves

We describe a large class of solutions in pure gravity, dilaton gravity and supergravity corresponding to extended higher-dimensional black holes with strong (non-linear) gravitational waves propagating along their worldvolume. For pure gravity, the extended black holes are higher-dimensional analogs of the point-like Schwarzschild black hole in four dimensions. For supergravity, they are non-extremal p-branes. The gravitational waves can be both space-filling and localized around the worldvolume of the extended black holes. The solutions we present contain a large number of arbitrary functions of the light-cone time describing the amplitudes of different non-linear gravitational wave modes.