Light wave behavior at and near a black hole event horizon?
"Any comparison to hydraulic waves, in particular Hydraulic Jump, Sub-Critical Flow and Super-Critical Flow? " Not really. The fundamental issue is that light is not a fluid so it does not obey the Navier-Stokes equations that govern fluid flow. Being that light does not obey those equations, it does not make sense to use things derived from those equations (e.g., the Froude number governing flow type) to model the behavior of light. "Any theoretical physicist writing on how waves waves behave near the event horizon ...". Very doubtful; we already know how things would behave. If you take a massive object, like a planet, then every point in space around that object has an "escape velocity" associated with it, where "escape velocity" is the speed at which you would have to throw something in order for it to never come back down to the massive object. The event horizon of a black hole is where the escape velocity equals the speed of light; it is just some imaginary line and not a physical surface. To help clarify, say you are in some sort of space capsule performing experiments with waves (light or otherwise), and are falling towards a black hole with an event horizon that is 1 light year from the black hole's center (so tidal forces are negligible at the event horizon). You would not notice anything special happening in your experiments as you passed the point where the escape velocity is 10 mph nor would you as you passed the point where the escape velocity is the speed of light; they are just imaginary lines that we use to describe what ultimately happens to objects. The only difference between the line where the escape velocity is 10 mph and where it is the speed of light is that your fate is sealed when you pass the latter. Good questions though; keep on thinking!
Absolutely not. Light wave behavior at or near the event horizon of a black hole is very simple and doesn’t need anything other than basic general relativity and electromagnetism to model. Light behaves exactly the same in a gravitational field around the event horizon as it does in the absence of a gravitational field. If you and the light were in a small region near the event horizon, you would see no difference. Light would still travel at ‘c’ and it’s frequency and wavelength would be unchanged. The reason for this is a simple consequence of general relativity. The smaller the region of spacetime observed, the flatter and flatter it looks. In a sufficiently small region, it will look as it does in the absence of a gravitational field. Because spacetime becomes flatter and flatter as you shrink down the region of spacetime you are observing, physics is simple locally. Things are much different at larger scales. If you were an observer in flat spacetime far away from the black hole observing light near the event horizon, you would see light behave in a different manner. You would see it’s wavelength get longer and longer, and you would measure its velocity at much less than the speed of light. This is because of the difference between how you measure spacetime at the black hole compared to how you measure it far away from the black hole. Your MEASUREMENTS don’t change it’s behaviour at the event horizon. So, classical general relativity and electromagnetism fully explain the behavior of light.
Some scientists try to model black holes this way. But a model is just a model. Its not the real thing. It might demonstrate some properties of light near a black hole, but not all properties. Don't take the analogy literally.
Light waves ate different from sound and waves in fluids and gases. Sound waves and hydraulic waves are longitudinal waves that require a medium where the atoms and molecules can be pulled apart and pushed together. Light waves are compound transverse waves with an electric wave perpendicular to a magnetic field that travels in a direction perpendicular to the to the force fields. No medium is required. The speed of light is NOT constant. Light is also particles of quantized energy called photons. Black holes and event horizons do NOT "suck." Sucking implies a difference in pressure. Pressure is force field to. Stars are hydrostatic equilibrium with gravity acting toward the core balanced by equal but opposite force of pressure acting in all directions. In that sense, yes, hydraulic fluid waves CAN be used as a model. There's a whole field of theoretical physics and engineering called helioseismology, as well as geophysics.