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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:

  1. Are there GW spheres just like photon spheres around a black hole?
Árpád Szendrei
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  • I've removed some comments that answered the question, and replies to them. – rob Jan 31 '20 at 19:22
  • Seems the same as https://physics.stackexchange.com/questions/368435/can-gravitational-waves-orbit-a-black-hole – ProfRob Apr 28 '22 at 11:37

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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.

Yukterez
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  • Thank you so much. "photons can be treated as single small test particles while gravitational waves are spread out far in practice they will just get fanned apart." Can you please elaborate on this? – Árpád Szendrei Feb 01 '20 at 04:55
  • In GR we tread photons as point particles, but GWs are treated as continuous geometry waves. In QM however you can tread a GW as a bunch of Gravitons, but don't ask me how. I don't know if there are valid combinations of GR and QM in the strong field – Yukterez Feb 01 '20 at 05:36
  • A sufficiently small wave packet of GWs (or any massless field for that matter) can be (approximately) described using geometric optics, meaning that it will follow lightlike geodesics. – TimRias Feb 06 '20 at 10:17
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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.

Yukterez
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anna v
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  • thank you so much. Do I understand correctly that this gravitosphere would not be detectable? – Árpád Szendrei Jan 31 '20 at 18:03
  • we have not even seen a photosphere. To detect gravitons would be a miracle, but who knows in the future? – anna v Jan 31 '20 at 18:39
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    Note that in English, "photosphere" is the surface layer of a star where the last scattering of light occurs. The unstable orbits of massless particles around a Schwartzchild black hole form the "photon sphere." The answer is right, though. – rob Jan 31 '20 at 19:24
  • That's true, I hope anna v won't mind if I edit and correct that. Other than that, the answer is correct. – Yukterez Feb 01 '20 at 02:35
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    There's nothing in the derivation of the photon sphere requiring or using quantum mechanics: https://en.m.wikipedia.org/wiki/Photon_sphere. It should apply equally well to any electromagnetic oscillation. – dllahr Feb 01 '20 at 02:36
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    QM is only needed if you interpret GWs as gravitons – Yukterez Feb 01 '20 at 02:38
  • @dllahr In the links I gave, the hawking radiation was derived using an effective gravitationa quantization, which means gravitons.,( I do not know if Hawking radiation can aso be derived using classical EM.) . The photon sphere is derived using photons, which again is the quantized stateof EM, so by analogy I anwered in the effective quantization frame. – anna v Feb 01 '20 at 04:15
  • @Yukterez thanks for the correction – anna v Feb 01 '20 at 04:18
  • @annav be that as it may, there's also derivation of the photon sphere w/o recourse to quantum mechanics – dllahr Feb 03 '20 at 02:24
  • @dllahr I could not find a link while googling, that gives what you claim. Can you give a link? – anna v Feb 03 '20 at 04:41
  • @annav The section in "Derivation for Schwarzchild black hole" in the wikipedia link above is what I was referring to – dllahr Feb 03 '20 at 09:57
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    The photon sphere is a classical (relativistic) phenomenon (i.e. there exist lightlike bound orbits around black holes.) It has literally nothing to do with Hawking radiation or quantum physics. – TimRias Feb 06 '20 at 10:13
  • @mmeent mainstream physics assumes that the underlying level of all nature is quantum mechanical, that is why there is such an effort to quantize gravity definitively. Thus, it make no difference that I give an explanation in terms of quantum mechanics, particularly so,since it is called a "photon" sphere and photons are quantum mechanical particles, and afaik there are no zero mass "particles" in classical physics . I would be grateful if you give me a link where I can see how the photon sphere is derived with GR and classical electrodynamics only. – anna v Feb 06 '20 at 17:10
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    @annav Almost any textbook treatment of black holes will cover the derivation of lightlike bound orbits, a.k.a. the light ring or photonsphere. See the work of Weatherall and Geroch for a mathematically rigorous proof that sufficiently compact wavepackets of any (classical) massless field (satisfy appropriate energy conditions) follow lightlike geodesics. – TimRias Feb 07 '20 at 07:24
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    @annav Even if you would insist on a quantum mechanical treatment, the (non)existence of the equivalent of a photonsphere for gravitons would have absolutely nothing to do with Hawking radiation. For example, it is possible (at least theoretically) to have ultracompact objects that are compact enough to have a photonsphere but not compact enough to collapse to a black hole and have an event horizon. The absence of an event horizon also means that there would be no Hawking radiation. – TimRias Feb 07 '20 at 07:30