Gravitational waves in strong field limit.

Apologies in advance if this is a "newbie" question, but in the
presence of strong gravitational fields, will gravitational waves start
interacting with each other, to the extent that gravitational collapse
may take place?

Alternatively, or additionally, could this also be true if there many
strong localised curvature perturbations (localised solitons?)
introduced into the metric? If I were to agitate the surface of the
spacetime pond by throwing in many thousands of large pebbles, could
the resulting ripples coallesce to form a black hole? (I am assuming
absence of massive particles throughout).

Any references would be appreciated.

- Sabbir.

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