# Converging light

Imagine that we emit a light pulse. As is the nature of light, it will expand. However, light is affected by gravitational fields and light has its own. Therefore, will the light converge given infinite time and infinite distance to travel interrupted?

• No. Even if I accept that two photons traveling in parallel would attract (I am not sure I do), you could not get them close and parallel enough that the force would bring them together faster than their momentum causes them to drift apart. Uncertainty in lateral momentum from Heisenberg... – Floris May 6 '15 at 3:57
• One can do self-focusing of light in non-linear media... I don't know if it happens in the vacuum. If it does, it doesn't happen because of gravity but because of QED. – CuriousOne May 6 '15 at 4:33
• It was observed that two photons could travel together, see photon bunching. And the photons in a radio wave are aligned too in their B and E field components. But converging of a light beam was not observed and is not possible as I know – HolgerFiedler May 6 '15 at 5:21

No, or at least not under normal circumstances.

Calculating the gravitational force between light beams turns out to be rather complicated, so let's use an analogous but simpler system. Instead of a spherically symmetric pulse of light consider an explosion that throws out a spherically symmetric cloud of light particles.

At any time $t$ the cloud of particles will have some radius $r(t)$ and total mass $m$, so the escape velocity at the surface of the cloud is just:

$$v_e = \sqrt{\frac{2Gm}{r(t)}}$$

If the velocity of the particles is greater than $v_e$ then the cloud will carry on expanding forver. If the velocity is less than $v_e$ the cloud will recollapse. So whether the cloud expands forever depends on how great the particle velocity is compared to the gravitational forces. The fact that a gravitational force exists does not necessarily mean the cloud must recollapse.

Now consider our light pulse. Unless the intensity of the light is so great that it creates a black hole the escape velocity will always be less than $c$ and the light will escape to infinity.

If you're interested in some background then have a look at the question Do two beams of light attract each other in general theory of relativity?. In particular note that parallel light rays do not attract each other due to gravity so a parallel ray of light will not gravitationally focus itself.

• parallel beams are not attracted at all this is correct, but that doesn't mean that the wavefront doesn't collective attract itself, as long as the wavefront curvature is significant (near the Rayleigh range) while still being asymmetric (a spherically symmetric wavefront would cancel all its contributions to curvature) , and the intensity is high enough, there should be some effect of self-gravitation on the wavefront curvature – diffeomorphism Jun 1 '15 at 18:53