Is the formation of bound states from light-light scattering or from the scattering of gravitational waves possible according to general relativity? If it's possible, are there papers out there about it? And are some of those bound states black hole-like? I'm not talking about realistic light, like a world without fermions or other things that aren't gravity. Also, it's a world without quantum mechanics.
We normally describe gravitational waves using the linear approximation and in this approximation gravitational waves simply superpose rather than interacting so no bound state is possible. However the energy in the GWs does contribute to the curvature so once you move past the linear approximation the waves do interact and could in principle form a bound state.
These bound states are generally called geons and there has been a lot of research into whether they can exist or not. This isn't an area I know a lot about but the impression I get is that research has stalled a bit. We know geon solutions must exist but we don't know if they are stable.
Wikipedia uses the term geon to refer to bound states of light as well. There is also the kugelblitz, which might also fit your criteria.