Could we move a spaceship by moving a Black Hole? What if a spacecraft were dragged by a black hole, and the black hole were pushed by continuously firing lasers into it?
Would this allow the ship to be accelerated faster than laser propulsion, which could only safely accelerate the ship at 1 g or slightly higher, while the black hole could (conceptually) be accelerated at much higher speeds, and the trailing spaceship would accelerate towards it in constant free fall, as oppose to suffering high G forces?
I'm aware this would all take literally astronomical amounts of energy, but conceptually?
 A: Pushing the black hole means pushing both the ship and the black hole, because the ship is part of the system.  That uses more energy than just pushing the ship itself with lasers (or whatever).  You've just added extra mass to push by adding the black hole.
A: Yes, we can move a spaceship by moving a black hole, but the best approach is not the one you described. The idea of using a black hole to power a spacecraft has been seriously proposed and studied in some detail:
https://arxiv.org/abs/0908.1803
From a practical standpoint the size of the black hole is very small and the size of the spacecraft is relatively large. So you will not get the black hole accelerating the craft gravitationally. Instead, the black hole acts as a reaction furnace which takes in matter and spits out energetic radiation, which is then used to give thrust to the spacecraft and the black hole together.
A: Spaghettification what will happen to an astronaut free falling into a black hole,

is the vertical stretching and horizontal compression of objects into long thin shapes (rather like spaghetti) in a very strong non-homogeneous gravitational field; it is caused by extreme tidal forces. In the most extreme cases, near black holes, the stretching is so powerful that no object can withstand it, no matter how strong its components. Within a small region the horizontal compression balances the vertical stretching so that small objects being spaghettified experience no net change in volume.


Stephen Hawking described the flight of a fictional astronaut who, passing within a black hole's event horizon, is "stretched like spaghetti" by the gravitational gradient (difference in strength) from head to toe. The reason this happens would be that the gravity force exerted by the singularity would be much stronger at one end of the body than the other. If one were to fall into a black hole feet first, the gravity at their feet would be much stronger than at their head, causing the person to be vertically stretched. Along with that, the right side of the body will be pulled to the left, and the left side of the body will be pulled to the right, horizontally compressing the person.

So,  the free fall  must be at such distance  that the astronauts would not suffer bodily harm, very far away from the strong gravitational fields of the black hole.
A: I interpret the question as: "Can you orbit an accelerating black hole?"
The answer to this question is: That depends on the acceleration.
There is a well known analytic solution to the vacuum Einstein equation, known as the "C-metric". In this metric the acceleration is power not by a laser (as in the OP's question), but by a conic singularity (i.e. cosmic string) "pulling" or "pushing" the black hole. (However, the exact source of the acceleration should make little difference.)
The existince of stable orbits around the black hole in the C-metric was investigate in this paper: [1405.2611]. They conclude that stable circular orbits exist as long as:
$$ a < 0.0045396037095\frac{c^4}{2GM}$$
For a black hole with a Schwartzschild radius of about 1 meter, this works out to about $4\times 10^{14}$ m/s^2 or $4\times 10^{13} g$.
As an object orbiting the black hole is in free fall, it would not suffer from the acceleration. (Although I have not looked at the tidal forces involved.)
Now, only for the trivial matter of accelerating the black hole at this rate...
