Quick Questions, Short Answers - No Debate

Good questions. Answers in reverse order:For the basic Schwarzschild (non-rotating, non-charged) black hole, there is a photon orbit 50% further out than the event horizon. If you were to stand at a point on this orbit and look tangentially to the black hole, you will see the back of your head Plus an infinite number of repeats disappearing into the distance. If you build a hollow tube space-station around the black hole and centre it on the photon orbit, the tube will look straight to anyone on the inside. If the station is placed inside the photon orbit, it will look curved again - only it will curve away from the black hole!!Now a Lagrange point is a very specifically defined concept within Newtonian Gravitation, and it doesn't readily apply to photons - but, if you are simply asking if there is a place in the vicinity of a black hole where a photon can remain stationary, then the answer is, yes! In fact, owing to the spherical symmetry of the black hole, there must be an entire sphere of these places. And this sphere is our infamous event horizon. The horizon is actually a (spherical) sheet of trapped photons. What is more, this must mean that the horizon must be travelling at the speed of light - and it is. In fact, all of the relativistic effects around the black hole that you call gravitational, can just as easily be understood in terms of relativistic velocity.I guess any more than that would really need its own thread... and my chilli salmon is calling.

When well separated, black holes behave just as normal gravitating objects. If you squash the Sun down to within its Schwarzschild radius, it will collapse to a black hole, but the Earth will continue to orbit as normal. And if you then squash the Earth down to a black hole, the moon will continue to orbit, without any change. And the Earth-Sun and Earth-Moon Lagrance points will be unaffected.A small black hole can certainly find itself located at (or orbiting around) a Lagrange point, just the same as any test mass.Two black holes in binary orbit that are close enough for us to wonder about their effect on their own Lagrange points are almost certainly in the midst of ultra rapid spindown towards merging, throwing out enormous quantities of gravitational radiation. As the black holes merge, the local space-time becomes highly chaotic, and the Lagrange points simply get caught up in the maelstrom. Eventually, things settle down to (most likely) a spinning Kerr black hole.

I'm a bit confused by the question. If you are asking whether L4 and L5 could ever have a potential gradient so sharp that it creates a trapped surface and possibly an event horizon, then no, I am fairly sure that could not happen. That is why I mentioned the binary merger - that would create the most extreme potential gradients around L4 and L5. L1-3 are of course saddle-point unstable so they don't even act like gravitating points.

No Yes. e.g. -> by emission of a neutron At a basic level, the neutrons are there to buffer the repulsive nature of a bunch of positively charged protons, allowing the nuclear force to dominate over a much larger distance scale than normal, countering the electromagnatic force. Too many neutrons, and the effective nuclear force at the "surface" of the nucleus becomes "repulsive". But this is all a fair amount of handwaving to describe the effect of some hideously complex chromodynamics which is best left to the lattice boys and girls - certainly not for me!

Yes, I think that is an accurate statement