Black holes are unreachable hyperspheres.
This is why it's totally impossible to reach the event horizon of a black hole. When a black hole forms it sends out a gravitational wave (which is just a change in the amount of gravity present in a particular area) which moves outwards at the speed of light. Behind this wave is the black hole.
If you were right next to it when it forms then then you wouldn't see it expand because information can only travel at the speed of light, so it would be at it's maximum size the moment you become aware of it. The wave continues outwards for ever but after the strength of gravity is no longer enough to accelerate objects to light speed it stops being the wave front of a black hole and becomes an ordinary gravitational wave. The black hole then rushes back inwards at the speed of light which makes the black hole a perfect four dimensional (the fourth being time, so its life span) sphere. Its life span increases as you move away from it because of time dilation. This should be easily provable by monitoring the rate that black holes loose mass over time.
The problem with general relativity is that it views objects in free-fall as equivalent to objects at rest in the absence of gravity rather than equivalent to accelerated objects (the acceleration of gravity is felt as tidal force) and it views black holes as having expanding horizons from the perspective of objects falling towards them, when in fact their horizons are always moving inwards by the time any object becomes aware of them. You simply can't reach the speed of light and that applies to gravity as well. You will never have enough time to reach the event horizon of a black hole because time dilation shortens the life span of any object approaching a horizon that that's rushing inwards at the speed of light locally, so you couldn't catch up to it even if you were to accelerate towards it.