So the question then remains: what speed would it travel at?

it could be observed traveling at any speed < c depending on the relative velocity between it and the observer

It's worth highlighting that 1. $E = mc^2 + \hbar \omega$ 2. There are other factors that need to be conserved; largely spin - resulting in anti-matter being created as well as matter 3. This matter/anti matter would re-combine rather quickly and re-emit photons 4. I strongly suspect that the presence of the anti-matter will prevent a black hole from ever being created in the first place

The answers perfectly illustrates the confusion caused by the cabal who dictated that henceforth "mass" no longer means "relativistic mass" as it did when I was young, but "rest mass". Not only is rest mass not preserved, it also fails to be additive: two photons travelling in opposite directions each separately have no rest mass, but together they do. If one simply accepts that mass is just an equivalent for energy, then it does have all the nice properties one is used to.

@jk. Any speed at random? I think orlp's question could be more accurately phrased as "How can one determine the rest frame of such a black hole, given that there's no "natural" rest frame for any of the individual photons which go into making it?"

@R.M. the rest frame of the black hole made from photons would be the frame in which the total momentum of the photons was zero. Although photons have no rest mass they have a well defined momentum so there is a well defined zero momentum frame.

@UKMonkey 2. There are other factors that need to be conserved; largely spin - resulting in anti-matter being created as well as matter It's not clear to me what you're talking about. Why do you say matter (and antimatter) would be created?

@PM2Ring en.wikipedia.org/wiki/Matter_creation In short - there are many equations that hold in matter creation, not just matter energy equivalency.

@JohnRennie So if the black hole was formed from photons traveling almost the same direction, the resulting black hole would be traveling at almost the speed of light in that direction?

@JohnRennie I'm also having trouble visualizing a reference frame where the total momentum of all photons would be zero if none of the photons were traveling in opposite directions. Isn't the speed of light the same in all reference frames? You can't have a reference frame that "outruns" the intersecting beams of photons such that some beams are approaching from opposite directions, can you?

@PM2Ring Some other links that might help - or just help confuse. en.wikipedia.org/wiki/Spin_(physics) en.wikipedia.org/wiki/Color_charge

@UKMonkey I guess you're implying that the extreme photon density will lead to some pair production. I guess that's reasonable. But in that case, this is probably a more relevant link: en.wikipedia.org/wiki/Two-photon_physics ;)

@PM2Ring I'm saying that it's a prerequisite for a black hole; since they have mass; and the OP wants to make one with light; and that the first link I gave is the most relevant as the "matter creation" mentioned in yours is just that. The point is you asked why does matter have to be created in pairs, to which the answer is "many reasons"

@Ajedi32 Boosting between reference frames definitely changes the apparent direction that a photon travels. This fact is the basic foundation for the usual derivation of time dilation, with the light-clock on a train: in the light-clock's rest frame, the photon travels vertically up and down, while in a boosted frame, the photon follows a diagonal path as the train moves.

@probably_someone Ah, I think I get it! As long as the angle of intersection is non-zero, there is a reference frame where the two photons are approaching from opposite directions. In that reference frame the two photons would have very little energy if the angle was shallow (like, say, 1 degrees) so you'd need an absurd amount of energy to create a black hole from photons approaching each other at that angle. The resulting black hole would be traveling near the speed of light, with its total kinetic energy proportional to the increased amount of energy needed for its formation. Correct?

@Ajedi32 In a word, yes; the black hole's mass would correspond to the energy of the system in the center-of-momentum frame, and the black hole's kinetic energy would correspond to its total energy in the "lab" frame minus its mass. As far as the claim goes that you would "need an absurd amount of energy to create one at that angle," it's true only if there's some minimum mass at which you start creating one. As far as I can tell, we don't know enough about quantum gravity yet to know for sure if that's the threshold governing their creation.

@UKMonkey The point is you asked why does matter have to be created in pairs No, I didn't! You've misunderstood what I wrote.

@probably I've read that the smallest possible black hole would have a mass on the order of the Planck mass. I suspect you'd need to aim for something larger so that it doesn't immediately evaporate... assuming Hawking radiation is real (we need quantum gravity to be certain of that).

Now wait just one minute here - because my mind is reeling! What sort of matter would 'condensed' light create - quarks, electrons? Is a black hole more dense and more compact than a neutron star or is it just a large neutron star and the mass at the heart of a black hole is just neutrons?