# Gravitational waves cause by photons?

I was reading this question (Why does Light get caught by Gravity, when both are travelling at the Speed of Light?) and it brought me to the following:

Can photons create gravitational waves?

My rationale here is:

(1) although photos have no mass, they do have momentum (and I've always been a bit confused by this - how it works, etc.). It is an acceleration of mass that is required specifically to cause gravitational waves or would an acceleration of photon count as well?

(2) does a change of direction constitute a change of acceleration (eg, a photon on the edge of a gravity well of a black hole)?

(3) if (1) and (2) are both possible, then am I correct in thinking this means a photon does cause a gravitational wave?

• see this arxiv.org/abs/2001.10196 Jun 14, 2020 at 18:24
• @user6916458: Are you asking whether or not two photons attract each another due to their mutually curved space-time, are you asking whether or not they are able to generate detectable gravitational waves, or are you asking something completely different? Jun 14, 2020 at 18:38
• You might be interested in the Aichelburg-Sexl metric. The original reference is On the gravitational field of a massless particle. Jun 14, 2020 at 18:49
• @Semoi I'm not concerned about detectability, but whether the effect should excists Jun 15, 2020 at 7:17

Do two photons interact gravitationally?

Yes, they do. The simple picture is that photons have energy $$E=\hbar \omega$$ and that this leads to a mass, $$m=E/c^2$$. Therefore, two phonons attract each another by curving the space-time. The more complex description uses the energy-momentum tensor of general relativity theory.

Does photons generate gravitational waves?

Although photons do disturb space-time, I would not call this disturbances a gravitational wave. E.g. the Ligo project writes:

Gravitational waves are 'ripples' in space-time caused by some of the most violent and energetic processes in the Universe. Albert Einstein predicted the existence of gravitational waves in 1916 in his general theory of relativity. Einstein's mathematics showed that massive accelerating objects (such as neutron stars or black holes orbiting each other) would disrupt space-time in such a way that 'waves' of undulating space-time would propagate in all directions away from the source.

Since photons are not in this line of thought it seams to be wrong to call their gravitational effect a gravitational wave.

• I'm not sure I buy this. Are you sure there aren't solutions to the Maxwell-Einstein equations containing gravitational waves? I don't know, but I guess this is the question at hand.
– d_b
Jun 15, 2020 at 10:32
• If this is the question, I completely misunderstood it. @user6916458 could you please clarify your question. Jun 15, 2020 at 17:24