electromagnetic radiation - Do two beams of light attract each other in general theory of relativity?

In general relativity, light is subject to gravitational pull. Does light generate gravitational pull, and do two beams of light attract each other?

Answer

The general answer is "it depends." Light has energy, momentum, and puts a pressure in the direction of motion, and these are all equal in magnitude (in units of c = 1). All of these things contribute to the stress-energy tensor, so by the Einstein field equation, it is unambiguous to say that light produces gravitational effects.

However, the relationship between energy, momentum, and pressure in the direction of propagation leads to some effects which might not otherwise be expected. The most famous is that the deflection of light by matter happens at exactly twice the amount predicted by a massive particle, at least in the sense that in linearized GTR, ignoring the pressure term halves the effect (one can also compare it a naive model of a massive particle at the speed of light in Newtonian gravity, and again the GTR result is exactly twice that).

Similarly, antiparallel (opposite direction) light beams attract each other by four times the naive (pressureless or Newtonian) expectation, while parallel (same direction) light beams do not attract each other at all. A good paper to start with is: Tolman R.C., Ehrenfest P., and Podolsky B., Phys. Rev. 37 (1931) 602. Something one might worry about is whether the result is true to higher orders as well, but the light beams would have to be extremely intense for them to matter. The first order (linearized) effect between light beams is already extremely small.