[evan_au]

And what of the state of neutron stars? They are seen, yet the matter is very abnormal, what laws explain these adequatley

Neutron stars have a density which is high (about the density of a Uranium nucleus), but a mass which is low enough that the escape velocity is less than c, so light can escape.
- So you don't get the infinities associated with a black hole.
- Studies at LHC guide the understanding of the state of matter under these incredible densities

You need general relativity to explain them:
- Gravitational waves were first observed/deduced from the motion of orbiting neutron stars
- The NICER X-Ray telescope on the ISS is studying neutron stars to work out their density more accurately. You can see more than just the "near" side of the neutron star because gravitation bends light around them.
- It is thought that when the mass of a neutron star exceeds a certain critical mass & density, it will collapse into a black hole. NICER is trying to work out what that limit is.

See: https://en.wikipedia.org/wiki/Hulse%E2%80%93Taylor_binary
https://en.wikipedia.org/wiki/Neutron_Star_Interior_Composition_Explorer

[Eternal Student]

Hi Petrochemicals.  I hope you are well.

   I think evan_au has put in a sensible reply to most of your questions.

You also mentioned jets that appear to move faster than the speed of light.  You may need to find references for this but if it is what I think you are talking about then this occurs when the jets are moving close to the speed of light but at an angle that is almost directly toward the observer.  In such cases it has often been the case that Astronomers analysed only the tangential movement (or falsely projected the movement onto the sky).
Very briefly, draw a diagram and notice that the jet is much closer to the observer after it has appeared to move across the sky by one degree.  If the jet was travelling toward the observer at almost c then the light from the jet emitted at the end of the observation will strike the observer only a short time after the light emitted at the beginning of the observation.  The astronomer will often calculate the tangential distance covered incorrectly by observing that the jet covered one degree across the sky in almost no time at all and (falsely) assuming the distance to the jet remained reasonably constant over that time.
                     

[yor_on]

We could mention that Einstein found the idea of BH rather intimidating. He went from questioning their existence to accepting, and as I seem to remember, doing it on several occasions, before finally accepting it.

[evan_au]

And jets seem to defy light speed limitations

Eternal Student gave the explanation for this, but he omitted the not-so-obvious name for them: Superluminal Jets.

Find out more here: https://en.wikipedia.org/wiki/Superluminal_motion

[TommyJ]

Strangely, there was no obvious breakdown. Einstein began with a series of thought experiments that led to predictions of phenomena that had not previously been observed (gravitational lensing, time dilatation) or considered more than curiosities (kinetic energy of nuclear decay particles). Newtonian physics still dominates everyday engineering and remains an entirely valid approximation where v<<c.
[/quote]
Physics rather indoctrinate and make approximation than breakdown. Also black holes quite defy mathematics:
https://www.bbc.com/future/article/20201008-the-weird-mathematics-that-explains-black-holes-exist