# Can gravitational lensing also applied to gravitational wave?

We know light travels in a straight line but spacetime around an object with mass is curved, anyhow I'm wondering gravitational wave going at speed of light could also be bended by stars and probably black hole?

I read some similar question and the answer are mixed but mostly yes, is it because that's the way how all waves behaved?

Of course no experiment or observation has yet been done that can answer your question, so any answer you're given will be based on theory -- and not everyone adheres to the same theory.

There is pretty convincing evidence that gravitational waves carry positive energy (e.g., the "chirp" observed in gravitational waves that result from black hole mergers or neutron star mergers indicates that gravitational waves carry energy away from the system). Because energy acts as a source of gravity just like mass does, a reasonable guess is that the path of a positive-energy gravitational wave will be bent as it passes a black hole pretty much the same way a light wave's path is bent.

Another good argument is this: if gravitational waves move at the speed of light they must follow null geodesics the same way light waves do -- in other words, they should follow the same kind of path as a light wave propagating in a vacuum.

• Wouldn't even zero mass waves be bent? The mass is not doing anything if we are ignoring back reaction. I think the geodesic argument is enough. Dec 13, 2018 at 9:15
• Sure, zero mass waves would be bent-- and waves that move at the speed of light are necessarily zero mass. Dec 13, 2018 at 13:56

This is worked out to some degree in detail in MTW Gravitation, a classic text. There is a whole section on the bending of GW paths in the presence on a strongly curved background. The basic approach is the same as for GW on a flat BG. You assume a BG metric and do perturbation theory with a weak fluctuation on top of that . What you get are the equations for propagation of the GW on a curved BG space-time. All the same lensing effects follow as with the EM field. An another note the same applies to any hyperbolic PDE. BG solutions produce an effective metric and waves on top behave as Null Geodesics of that Lorentzian metric space. This was the impetus behind analog models of black holes in the 80s by Unruh, and later by Visser. It applies to acoustics and optics in a refractive media.

• What does "BG" mean? Dec 13, 2018 at 5:15
• BG = background, a common shorthand for the term. GW = gravitational wave, etc.
– user196418
Dec 13, 2018 at 11:48