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Can a wave exist within a black hole? A wave implies motion (amplitude and frequency) but motion can not occur without the passage of time. A wave also implies wavelength that cannot occur because gravity does not allow for any outward motion. Therefore, can a wave even exist inside a black hole?

In this forum we always speak of relative time and motion. But is there a relative timeframe if time is completely stopped? Can we speak of the frame of reference of being within a black hole if time does not move at all?

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  • $\begingroup$ Yes, every mass according to Einstein emits gravitational waves, including black holes. There's no restriction that gravitational waves must propagate only outwards from black hole, they can be emitted also inwards, inside black hole. $\endgroup$ May 14 '20 at 19:34
  • $\begingroup$ You should clarify what type of a black hole you are asking about, a real collapsed star or a mathematical abstraction like the Schwarzschild solution that cannot exist in reality. Real collapsars are empty with no possible motion inside for the exact reasons you stated. See this for details: math.stackexchange.com/questions/3310040 - Time does exist in hypothetical Schwarzschild black holes for a short duration, so motion is possible there before time ends, but these black holes don't exist in reality. Without stating, which black holes you have in mind, your question is unclear. $\endgroup$
    – safesphere
    May 15 '20 at 8:42
  • $\begingroup$ @safesphere I'm thinking of a real black hole. $\endgroup$ May 15 '20 at 17:42
  • $\begingroup$ @safesphere can you comment on the second paragraph of my OP. Can we speak of a frame of reference if time does not move at all? Or does it simply move into the realm of dividing by 0, so infinity? $\endgroup$ May 15 '20 at 17:58
  • $\begingroup$ A frame is a 4D coordinate system measuring space and time of a physical object (e.g. observer). Assuming no movement in time inside a collapsar: (1) all coordinate systems become 3D (space only) and (2) there are no physical objects (energy is zero) to attach a coordinate system to one to call it a "frame". In this sense there are no frames without time, although you still can have coordinate systems to measure distances between points in empty space just like on a clean sheet of paper. However, such a measurement is only hypothetical, as it can be done neither on the inside nor from outside. $\endgroup$
    – safesphere
    May 16 '20 at 3:44
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This is an underspecified question as such but still it can be answered by deconstructing the question by pointing out conceptual misunderstandings I guess. So I'll give it a go.

  1. Wave doesn't imply motion. Only mechanical waves imply motion. Electromagnetic waves are also waves and there is no motion associated with it. It simply consists of oscillations of electric and magnetic fields. However, you're right that you need a notion of time to have a notion of wave (although, this would be true of any physically meaningful notion, a physics without time is something not much imaginable)

  2. Time doesn't cease to exist in a black hole (except at singularity where we don't know what happens). Time certainly exists inside a blackhole. In fact, according to general relativity, you won't even notice that you crossed the horizon if you're falling into a large enough black hole.

  3. Yes, if you use the coordinates of an observer sitting at the asymptomatic infinity, it'd look like the time stops as you approach horizon and the metric blows up at the horizon. However, this is just a pathology of a bad coordinate system as has been well understood for a long time. If you choose a good set of coordinates such as the Kruskel coordinates, you see that nothing catastrophic happens at the horizon and an infalling observer wouldn't even notice that they have crossed the horizon as I mentioned.

  4. Finally, electromagnetic waves can obviously exist inside the blackhole. No electromagnetic wave can come outside of the blackhole but radiation can certainly fall into blackhole. For example, see, the ingoing Vaidya metric which is a blackhole solution with radiation falling into the blackhole.

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  • $\begingroup$ Thankyou. Can you please clarify, 1. if things are falling into a black hole at speed c, how can time exist? Is it not dilated to a full stop? 2. can you speak of the wave length question? Would not any wave attempting to leave the black hold just pile up on itself and have zero wave length? 3. Yes, you would not notice if you fell into a black hole, but if time has stopped, you would never know that it has stopped for you too. You wouldn't even have time to think a single thought? $\endgroup$ May 14 '20 at 19:34
  • $\begingroup$ @foolishmuse 1. There is no valid proper frame of something moving at the speed of light. So you're not allowed to talk about the frame of reference of light. This is a simple fact from special relativity having nothing to do with horizons or black holes. 2. As I said, no wave or particle or anything for that matter leave black holes but they can absolutely fall into it. [...] $\endgroup$
    – Dvij D.C.
    May 14 '20 at 19:43
  • $\begingroup$ [...] 3. When I say you wouldn't notice if you fell into a black holes, I meant you would be perfectly conscious with your clock ticking just fine and you wouldn't notice. Not because time stops and you stop thinking but because nothing special happens at horizon. $\endgroup$
    – Dvij D.C.
    May 14 '20 at 19:43
  • $\begingroup$ Clarification: when I say nothing special happens at horizon, that's a statement in general relativity. If you include quantum mechanics, a lot of controversial stuff might or might not happen at horizon depending on who has the good fortune of winning those sweet physics bets. ;) But if something special does happen at horizon, equivalence principle would have to be sacrificed so I'd personally bet otherwise. $\endgroup$
    – Dvij D.C.
    May 14 '20 at 19:45
  • $\begingroup$ @safesphere I already mentioned like two times that I'm limiting my answer to general relativity for it is not exactly settled how OP's questions regarding the horizon would be answered in quantum mechanics. Within general relativity, where is this non-outdated knowledge that would contradict the simple statement that you'd fall through the horizon of a blackhole smoothly? $\endgroup$
    – Dvij D.C.
    May 15 '20 at 12:08

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