Are there GW spheres like photon spheres around a black hole? I have read this question:
Are gravitational waves effected by the curvature of space time (gravitational lensing)?
Gravitational lensing of gravity
Can gravitational waves orbit a black hole?
This does not give a satisfactory answer.
Based on these answers, GWs should follow spacetime curvature just like EM waves.
Around a black hole, there is something called a photon sphere, where EM waves are in a stable orbit around the black hole.

A photon sphere[1] or photon circle[2] is an area or region of space where gravity is so strong that photons are forced to travel in orbits.

https://en.wikipedia.org/wiki/Photon_sphere
Could GWs be orbiting just like EM waves around a black hole?
Both GWs and EM waves do travel at the speed of light, so theoretically there could be a stable orbit.
Question:


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*Are there GW spheres just like photon spheres around a black hole?

 A: 
Could GWs be orbiting just like EM waves around a black hole?

In principle yes, but since photons can be treated as single small test particles while gravitational waves are spread out far in practice they will just get fanned apart. You can create linearly directed gravitational waves though, but in nature they are rather seldom.

Both GWs and EM waves do travel at the speed of light, so theoretically there could be a stable orbit.

The photon sphere is not a stable, but an unstable orbit. The last stable orbit for a Schwarzschild black hole is at r=6M, while the photon sphere is at r=3M. That means that all the photons travelling around the photon sphere will either plunge in or fly away sooner or later when the spacetime gets slightly perturbed or if they don't have the ideal initial conditions up to the last digit. Gravitational waves disturb the spacetime even more than photons, so there won't be too much revolutions around the photon sphere.

Tags: general relativity, quantum mechanics

My answer is only from the viewpoint of general relativity, since I don't know how to combine quantum mechanics with black holes.
A: To start with photons are quantum mechanical entities. It is called a photon sphere because it is photons that are trapped , and it is not described in terms of the emergent electromagnetic waves, afaik.
Gravitational waves are general relativity solutions and are classical. The  gauge boson for gravity once it is definitively quantized is the graviton, so it should be a gravitosphere not a gravity wave sphere.
Following the road of Hawking radiation, which also expects to have gravitons too, one can assume that some of them will be trapped the same way as the photons ( assuming that gravitons exist). See the links here.
