Orbiting spaceship just above a black hole horizon

[AndreiB]

The experiment I am thinking about is a spaceship that approaches the horizon of a supermassive black hole by firing its engines in the opposite direction of its motion. I have the following questions:

1. When the ship is in a stable orbit, just above the horizon, how would an observer far away from the black hole see it? Would it be stationary (almost) because of time dilation?

2. Is it possible for the ship to further decrease its orbit until it passes through the horizon? Would it continue to orbit inside the black hole?

3. If 2 is possible, why would the ship, by using the same amount of energy as in step 2, be able to raise its orbit again and get out of the black hole? The situation seems to be symmetrical.

 

[PeterDonis]

The experiment I am thinking about is a spaceship that approaches the horizon of a supermassive black hole by firing its engines in the opposite direction of its motion

This won't work. I suggest reading this Insights article of mine:

https://www.physicsforums.com/insights/centrifugal-force-reversal-near-black-hole/

1. When the ship is in a stable orbit, just above the horizon

There are no stable orbits just above the horizon. The closest stable orbit is at $r = 6M$. The closest circular orbit at all is the photon sphere at $r = 3M$, but orbits there are unstable.

2. Is it possible for the ship to further decrease its orbit until it passes through the horizon? Would it continue to orbit inside the black hole?

Since there aren't any orbits at all inside $r = 3M$, there certainly aren't inside $r = 2M$.

 

[AndreiB]

This won't work. I suggest reading this Insights article of mine:

https://www.physicsforums.com/insights/centrifugal-force-reversal-near-black-hole/

Thanks!