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.
On further checking I find a post today on sci.physics.relativity which somewhat confirms my guess and sheds more light on this:
: Two parallel beams of light do not attract each other. Two antiparallel
: beams of light do attract each other, with an attraction that's twice
: what one would expect by sticking a mass of E/c^2 into Newton's equation.
Perhaps beams which are crossing at an angle between 0 and 180 degrees would have an intermediate level of attraction (or else something more complicated happens...).
This does not make it clear whether crossing sufficiently intense light beams would form a black hole, though. The sci.physics.relativity FAQ says, at http://www.xs4all.nl/~johanw/PhysFAQ/black_fast.html:
: The statement that "If enough mass is squeezed into a sufficiently small
: space it will form a black hole" is rather vague. Crudely speaking we
: would say that if an amount of mass, M is contained within a sphere
: of radius 2GM/c2 (The Schwarzschild radius) then it must be a black
: hole. But this is based on a particular static solution to the Einstein
: field equations of general relativity and ignores momentum and angular
: momentum as well as the dynamics of space-time itself. In general
: relativity, gravity does not simply couple to mass as it does in the
: Newtonian theory of gravity. It also couples to momentum and momentum
: flow, the gravitational field is even coupled to itself. It is actually
: quite difficult to define the correct conditions for a black hole
: to form. Hawking and Penrose proved a number of useful singularities
: theorems about the formation of black holes, and from astrophysics we
: know that the theorems should apply to sufficiently massive stars when
: they reach the end of their life and collapse into a small volume.
Elsewhere they point out that the Big Bang, despite having densities high enough to put matter inside its Schwarzschild radius, did not form black holes, because of the tremendous outward velocity of the material.
In the case of photons, I worry that their very high velocities may mean that simple calculations of energy densities might not give the right answer for black hole formation. The question of black hole formation and dynamics is a difficult and active area of research.