Can light cause gravity?

Question

We know the following:

1. Two masses are attracted to one another, as represented by Newtonian gravity

   $F = \frac{GMm}{R^{2}}$

2. Light is massless and bends in the curvature of space-time which can be created by a mass, where the deflection is calculated with Einstein's general relativity and is twice that calculated by Newtonian gravity, https://en.wikipedia.org/wiki/Eddington_experiment.

3. $E = mc^{2}$, where m is the relativistic mass.

Is there something special about mass energy that produces a curvature of spacetime? If that rest mass energy were converted to light energy (say, by annihilation of an equally large amount of matter and anti-matter, a planet sized "anti-matter bomb"), would the spacetime curvature resulting from the originating mass essentially instantaneously disappear?

The inverse process, say through a "pair-production bomb," could instantaneously create space-time curvature. Of course, "instantaneous" here is nearly achieved anyway since the light source is traveling at the speed of light toward the about-to-be-born mass.

Of course, this also answers the question of whether light attracts itself (through "gravity").

Answer 1

The source of gravity is energy-momentum, not just mass. Light has energy-momentum so it is a source of gravity.

Answer 2

Yes. You can have, for example, a Friedmann universe filled with nothing but electromagnetic radiation. The light’s gravity, due to its energy-momentum tensor, is the only gravity determining the dynamics of that cosmology.

Our own universe, which we believe is homogeneous and isotropic on the largest scales and thus can be modeled using the Friedmann metric, had an early radiation-dominated phase. The gravity of electromagnetic radiation was very important in determining the rate of expansion during that phase. The “radiation” then also included ultrarelativistic particles with mass, so it wasn’t 100% “light”. But the form of its energy-momentum tensor, and thus its gravity, was almost the same as if it were, because everything was traveling either at or very near the speed of light.

Answer 3

Archibald Wheeler consider the simpler case than a kugelblitz, of a collection of photons dense enough to be gravitationally bound, which he called a geon. He thought they were extremely unlikely to be stable.

Photon-photon scattering can occur where combined energy is above that need for electron-positron pair production.