Anders Sandberg, <firstname.lastname@example.org>, writes:
> The mass of the energy is E/c^2, so it starts to have a noticeable
> gravitational pull as GE/c^2 becomes noticeable. As the energy goes up
> to the Planck energy density 1e28 g/cm light is definitely going to be
> behaving according to the superposition principle, the stream will
> have become associated with so much space-time curvatures that things
> turn weird. I guess it would be self-focussing, as a beam would have a
> radial pull inwards.
I am not sure about this, because in some ways the characteristics of a photon can be thought of as the limit of the case of a small mass particle moving closer and closer to the speed of light. For example, the ratio between (relativistic) energy and momentum of a particle is v, which approaches c as the particle approaches the speed of light. For photons, this ratio is exactly c.
Two particles travelling side by side do not experience gravitational attraction that increases as the velocity approaches c, even though their total energy increases. Two particles whizzing by at 99.99999+% of c may have "black-hole-ish" energy levels but are not attracted to each other much. If the analogy above holds water, then two photons with similar total energies travelling side by side will also fail to be attracted together.
I don't know how good this analogy is, but it is necessary to keep in mind that fast-moving particles may have very different gravitational effects than slow ones with equivalent total energies. They have large off-diagonal terms in the stress energy matrix which produce magnetic-like effects in the gravitational field that you don't see with stationary stources.