# Do electromagnetic waves interact with gravitational waves?

We know that electromagnetic waves travel the speed of light in space. Scientists have said that gravitational waves also propagate through space the speed of light. The movement of gravitational waves disrupts the space-time texture. Do electromagnetic waves disrupt the space-time texture too? And do electromagnetic waves interact with gravitational waves?

• What do you mean by "perturb the space-time"? – Señor O Jul 2 '17 at 21:44
• EM waves do influence spacetime geometry, yes. Basically, anything with nonzero energy-momentum tensor ($T_{\mu \nu}$) on the right side of Einstein's equations induces a non-flat spacetime. – Avantgarde Jul 2 '17 at 21:51
• This is a near duplicate of: physics.stackexchange.com/questions/247927/… Which doesn't have an answer – R. Rankin Jul 3 '17 at 8:25
• @R.Rankin: Not so sure it's a duplicate. That question is focused entirely on whether electromagnetic waves have their own gravitational perturbations associated with them, which is the first question asked here. The second question (whether EM waves are influenced by external gravitational waves) is unaddressed on that page. – Michael Seifert Jul 3 '17 at 16:52
• A worthwhile distinction: gravitational waves disrupt the 'space-time texture' insofar as they are disruptions in the space-time texture. Electromagnetic waves, on the other hand, disrupt the space-time texture insofar as they carry energy and momentum, which influence space-time through Einstein's equations. – gj255 Jul 3 '17 at 17:12

Yes, they interact, but it is only when it is a very weak interaction that one can say they interact, and they do so very weakly. In the strong wave domains their interactions are seen as consistent fully nonlinear solutions to the GR-Maxwell equations.

In linearized general relativity (GR, equivalently linearized gravity), they do not interact (but it depends on how you linearize). One can expand in higher order terms and they will then.

For the full nonlinear GR, the interaction is based on the EM wave having a stress energy tensor, on the RHS of the Einstein Field Equations, as

$G_{\mu\nu} = (T_{\mu\nu})_{EM}$

with the T tensor just due to the EM wave.

In GR these solutions are part of a set of so called electrovac solutions (a general case where the RHS is any consistent electromagnetic field, static or dynamic or both).

Electrovac solutions can be covariantly distinguished as radiative or not, depending on whether there are one or more null vectors associated with the EM field. [it is similar for GW solutions, they have to have some null vectors that are eigenvectors of the Weyl tensor]

See a good description at Wikipedia at https://en.m.wikipedia.org/wiki/Electrovacuum_solution

There are indeed some exact solutions which have been found which describe spacetimes which have both plane GW and EM waves, typically collinear. See those in what are pp (plane parallel waves) spacetimes, with the plane EM waves also, at https://en.m.wikipedia.org/wiki/Pp-wave_spacetime

It should be noted that finding exact solutions in GR, for electrovac or anything else, is not easy. It is in those exact solutions where the solution is dependent on both the EM and GW wave being there; in that sense you can note the interaction. If instead one tries linearizations it is possible to have one without the other (in the linearized regime because the interactions are so weak).

It is interesting that various aspects of EM waves in Minkowski spacetime need to hold the same in curved spacetime. You can see some of that in the two wiki articles, where for instance the symmetry group for the plane waves is indeed E(2), the Euclidian group in the orthogonal plane to the null vector.

For GWs in exact solutions, without EM, the pp spacetimes mentioned are example of so called Petrov Type N solutions, but it is possible to have other radiative solutions of different Petrov types. There's also exact solutions for pair of colliding plane waves. When they collide they also form non-null spacetimes inside the colliding regions. The links above talks about some of those, and you can google electrovac solutions.