# What is the interaction of gravitational waves?

Please excuse my lack of knowledge about the subject but, If gravitational waves travel thru the fabric of space time do they interact with each other? Meaning do they create interference patterns such as a typical wave? If not why not? And, the other part of my question is since strong sources of gravity curve space-time what effect does this have on a gravitational wave traveling thru the fabric of space time. Does this act as a damper and/or amplifier on the traveling wave or is it somehow isolated from the effect of the space time curvature.

• Gravitational waves are (almost) always treated perturbatively. This means you assume a fixed background $g^{0}$ and the gravitational wave is imposed onto that as a series expansion $g=g^{0}+\epsilon h+\epsilon^2 h^{(2)}+...$. Usually only the linear term $\epsilon h$ is kept. In this case, the waves do not interact (however note that interference is just linear superposition, it is usually not considered interaction). One can take interaction into account by considering higher order terms. As far as I can recall one can calculate interesting effects in this case, such as... Oct 18, 2018 at 17:30
• ... two waves meeting and upon interaction they form a black hole. Oct 18, 2018 at 17:30
• @Uldreth, isn't your 'comment' more of an answer than a comment? Oct 18, 2018 at 18:11
• "Does this act as a damper and/or amplifier" - Have you considered the curvature acting as a (gravitational) lens? Oct 18, 2018 at 23:07
• Light interference is linear, but what happens when two jects of water cross? Oct 18, 2018 at 23:22

## 1 Answer

Interference in most waves we are familiar with physics (e.g. EM waves, low intensity sound waves, small waves on a string, wave functions of particles etc.) obey a superposition principle which is what "wave interference" typically means. This is because the interactions which produce these waves are linear in the sense that two waves which overlap simply add (in amplitude) at each point. If you have a wave with amplitude A and another wave with amplitude B, then the maximum amplitude of a resulting interferred wave is A+B - it can't be 2(A+B) or some other such value.

Gravitational waves are solutions to the linearized version of General Relativity. As such, in this linear limit, they should behave just as other waves do. However, General Relativity itself is not a linear theory - so real gravitational waves (i.e. without making a linear approximation) would have "interference" in a non-linear fashion that's not really familiar from most of the physics we encounter in everyday life. If we are talking about very weak gravitational waves very-very far from the source (such as those detected by LIGO), then those gravitational waves should act just as any other waves do. They should interfere. If we get to strong-field regimes, then the problem becomes extremely complicated and we would have to resort to numerical simulations to tell us what would really happen.

With regards to how gravitational waves interact with matter: they interact with the gravitational field of matter of course. Matter produces a stress energy field which sources gravity. Again, since the equations of general relativity are non-linear, it is very non-trivial to figure out exactly what would happen when a real gravitational wave meets a strong source of gravity. Since the principle of superposition doesn't apply for non-linear systems, it would then become impossible to really disentangle the "gravitational wave" from the background "space-time curvature from a massive body" at that point. Unlike in E&M where you could just "add the two solutions together" (wave solution + static solution of a static charge), you can't simply do that in general relativity. In the weak field limit where the gravitational wave is extremely weak, I would expect the effects of a gravitational field on EM waves such as shapiro delay, redshifting, bending, etc. to apply to gravitational waves too...but unfortunately I can not recall an authoritative source that makes such a claim at this time.

• Interference is a superposition of coherent waves, no? Oct 18, 2018 at 23:16
• @safesphere Are you asking if interference is only possible with idealized sine-wave like waves? I guess I'm not really following where you're trying to go with the question. Oct 18, 2018 at 23:26
• A wave interferes only with itself, does it not? You can't get an interference pattern, unless the sources are synchronized. Oct 18, 2018 at 23:48