The reason given in most places about why one cannot escape out from an event horizon is the fact that the escape velocity at the event horizon is equal to the speed of light, and no one can go faster than speed of light.
But, you don't really need to reach the escape velocity to get away from a massive object like a planet. For example, a rocket leaving earth doesn't have escape velocity at launch, but it still can get away from earth since it has propulsion.
So, if a rocket is just inside the event horizon of a black hole, it doesn't need to have the escape velocity to get out, and it should at least be able to come out of the event horizon through propulsion. Also, if the black hole is sufficiently large, the gravitational force near the event horizon will be weaker, so a normal rocket should be able to get out easily.
Is this really theoretically possible? If it was just the escape velocity being too high was the problem of getting out, I don't see any reason why a rocket cannot get out.
This is a similar question, but my question is not about a ship with Alcubierre drive.
Best Answer
It is often said that the escape velocity at the event horizon is the speed of light, but while this is true in a sense it is not very useful. The problem is that the speed is an observer dependent quantity. An observer far from the black hole would say the escape velocity at the event horizon was zero, which is obviously nonsensical and proves only that speed is not a useful quantity to describe the motion near an event horizon.
There is more on this in the question Does light really travel more slowly near a massive body? though this may be excessively technical.
A better way to understand what is going on is to ask how powerful a rocket motor would you need to hover at a fixed distance from the black hole. For example to hover at the Earth's surface your rocket motor needs to be able to generate an acceleration of $g$ i.e. a force $mg$ where $m$ is the mass of the rocket. If your rocket motor is more powerful than this you will accelerate upwards away from the Earth and if it is less powerful you will fall downwards towards the Earth.
In Newtonian gravity the acceleration required to hover at a distance $r$ from a mass $M$ is given by the well known equation for Newtonian gravity:
$$ a = \frac{GM}{r^2} \tag{1} $$
The event horizon is at $r = 2GM/c^2$ so if Newtonian gravity applied we could substitute this into equation (1) to give:
$$ a = \frac{c^4}{2GM} \tag{2} $$
which is a large number, but some future physicist might be able to build a rocket that powerful. The problem is that when we move to general relativity equation (1) is no longer valid. The GR equivalent is derived in twistor59's answer to What is the weight equation through general relativity? The details are a little involved, but in GR the equation becomes:
$$ a = \frac{GM}{r^2} \frac{1}{\sqrt{1-\frac{2GM}{c^2r}}} \tag{3} $$
If you now substitute $r = 2GM/c^2$ into this equation you find that the acceleration required is infinite i.e. no matter how powerful a rocket motor you build you cannot hover at the event horizon. Once at the horizon you are doomed to fall in.
And this explains why you cannot start at the event horizon and move away from it slowly using your rocket motor. You would need an infinitely powerful rocket!