Lensing Gravitational Waves Like Light?

[sbrothy]

TL;DR Summary

Can GWs be focused like light?

I was reading (or at least skimming) this paper:

https://arxiv.org/abs/2005.10702

in which they seem to be discussing gravitational wave lensing. Is this an analogue of light lensing or is it another subject entirely? I mean, as I understand it, light is bend using gravity (as for example with Einstein Rings) but what would bend or focus a gravitational wave? I've probably misunderstood something here so bear with me a please. I'm just a curious amatoer fascinated by all the cool stuff going on in physics. In particular with gravitational wave experiments.

I'm probably not going to understand a detailed answer describing how, if it is indeed possible and I'm not really looking for such an answer although you're welcome to try me... :)

I'm more after a simple answer

 

[Ibix]

Gravitational waves can be gravitationally lensed, yes, at least in theory. I'm not aware of any actual observations of it, but it's early days in gravitational wave astronomy. Gravitational waves follow null paths through spacetime just like light does, so they are lensed just like light, by interacting with the gravitational field of whatever's doing the lensing (gravitational waves interacting gravitationally is one aspect of gravity that makes the maths so much trickier than light). From a skim of the abstract, the article you cite appears to be observing that gravitational waves from cosmological sources are much, much lower frequency than electromagnetic radiation from similar sources and noting that the lensing effect will be very different as a result.

 

[sbrothy]

Thank you, fascinating. So, gravitational waves are lensed/bent by... well, gravity?! I may be forgiven for thinking this sounded farfetched. I must really read more about this phenomenon.

 

[Ibix]

If gravitational waves weren't affected by static gravitational fields then you'd be able to tell the difference between "being stationary in a gravitational field" and "accelerating in a rocket in the absence of gravity". That would violate the equivalence principle, which is a founding principle of GR (at least, when formalised somewhat), so it'd be self-contradictory.

To explain - imagine that I'm in a box and feel proper acceleration. I place a source of electromagnetic waves on the floor and a detector on the ceiling. The waves are redshifted when detected. If I'm sitting on a planet, this is due to gravitational redshift. If I'm in a rocket in free space, this is because the waves take time to reach the ceiling and in that time the ceiling has accelerated a little and the waves are redshifted from velocity related Doppler. And if you follow through the maths you find that the amount of redshift is exactly the same, given equal "acceleration due to gravity" in the two situations. Thus I can't use this experiment to break the equivalence principle.

Now replace the EM source and sensor with a gravitational wave source and sensor (I'll leave the implementation details as an exercise for the reader, but this is possible in principle). In the rocket case the waves will be Doppler shifted for the exact same reason as the EM waves - the ceiling has accelerated by the time they are received. So in the sitting-on-a-planet case either the gravitational waves are gravitationally redshifted or I can tell the difference between the two situations in a closed-box experiment and GR is inconsistent. Also, if they aren't redshifted, I could get free energy by shining light down, gaining energy as it falls, and using that energy to power my gravitational wave source, which emits waves that don't lose energy as they climb back up, and using that energy to power my light source and skimming the extra.

Edit: if you find a gravitational wave source in a small box far-fetched, imagine a cosmological source that just happens to emit waves that pass through my box in an upwards direction, and have floor and ceiling mounted detectors.

 

[sbrothy]

If gravitational waves weren't affected by static gravitational fields then you'd be able to tell the difference between "being stationary in a gravitational field" and "accelerating in a rocket in the absence of gravity". That would violate the equivalence principle, which is a founding principle of GR (at least, when formalised somewhat), so it'd be self-contradictory.

To explain - imagine that I'm in a box and feel proper acceleration. I place a source of electromagnetic waves on the floor and a detector on the ceiling. The waves are redshifted when detected. If I'm sitting on a planet, this is due to gravitational redshift. If I'm in a rocket in free space, this is because the waves take time to reach the ceiling and in that time the ceiling has accelerated a little and the waves are redshifted from velocity related Doppler. And if you follow through the maths you find that the amount of redshift is exactly the same, given equal "acceleration due to gravity" in the two situations. Thus I can't use this experiment to break the equivalence principle.

Now replace the EM source and sensor with a gravitational wave source and sensor (I'll leave the implementation details as an exercise for the reader, but this is possible in principle). In the rocket case the waves will be Doppler shifted for the exact same reason as the EM waves - the ceiling has accelerated by the time they are received. So in the sitting-on-a-planet case either the gravitational waves are gravitationally redshifted or I can tell the difference between the two situations in a closed-box experiment and GR is inconsistent. Also, if they aren't redshifted, I could get free energy by shining light down, gaining energy as it falls, and using that energy to power my gravitational wave source, which emits waves that don't lose energy as they climb back up, and using that energy to power my light source and skimming the extra.

Edit: if you find a gravitational wave source in a small box far-fetched, imagine a cosmological source that just happens to emit waves that pass through my box in an upwards direction, and have floor and ceiling mounted detectors.

Oh, I hadn't noticed that you decided to try me with a more in-depth explanation after all. That actually makes perfect sense. Thank you. Not so farfetched after all then. The null-path following I can wrap my head around.

The next decade or so looks like it's going to be the golden age of large scale cosmomogical experiments (https://arxiv.org/abs/2005.10384). Excit8ng times... :)