The escape velocity for any object closer to the singularity than the event horizon is greater than c. However on the earth the escape velocity is 11.2 km/s, yet craft like the Voyager probes were definetly not launched with this velocity, they had a constant acceleration.

Lets take a Schwarzschild Black Hole with a diameter of 1 ly. Its mass would thus need to be 3.19e42 kg.

The acceleration due to gravity at the event horizon would be 9.5 m/s (a=G{M/r^2}), slightly less than than that on earth. The acceleration due to gravity one meter in from the event horizon of this supermassive black hole does not change appreciably.

Now a small craft launches a small object (say 1 kg) with a velocity of 100 m/s directly behind it (so aiming directly out of the event horizon). The distance the object travels before gravity stops it (v=0) can be calculated using the following equation:


From the point of release the objects moves 526 m, so thus the object gets 525 m from the event horizon. It escaped the event horizon! Without further propulsion being given to the object it would fall back to the black hole. But giving extra propulsion wouldn't be too hard.

So is it possible to escape the event horizon? Or have I missed something in my understanding of the problem?

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The object is yes moving toward the singularity, but is quickly accelerated to 100m/s after seperation from the mother craft.

Yes "d" is displacement. With 0 on the x-axis intersecting the event horizon. In displacement everything outside the event horizon is taken as positve, while between the event horizon and singularity is taken as negative.

In velocity/acceleration: negative is taken as velocity/acceleration toward the singularity. Positive velocity/acceleration is taken as away from the singularity.

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Alright forget about the launch of the small object. When d=-1 m, u=100m/s.

So one meter from the event horizon the small object is travelling at 100m/s away from the singularity.

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Any space craft ,would be accelerating toward the event horizon or the centre of the black hole.

Sorry. No.

You're using Newtonian physics in one of those rare instances where it gives the wrong answers.