If you think about the unstoppable collapse of a body to form a black hole, you might think that the body ends up with all its matter concentrated in a single point of space – the singularity. But again, this picture of the spacepoint-singularity residing in the center of the black hole is simply wrong. Using our analogy, you can see why. The singularity is the whole of the axis – and the axis represents a space direction. Hence, the singularity is not a point in space – it is infinitely extended!

This is exceedingly weird. From the outside, the region of a black hole looks like the surface of a sphere (in our model with two space dimensions and one time dimension, like the circumference of a circle). But inside that sphere, which has only a finite surface area, you can “hide” objects that are infinitely large – infinitely extended in space. How does this work? Again, it works because time and space trade places. Our simple scenario corresponds to an eternal black hole – a black hole that has always existed and will continue to exist indefinitely in the future. From the outside, the black hole is infinitely extended in time, but has only a finite size in space. Inside, the tables are turned: Time is only of finite extent (it starts at the horizon and ends abruptly at the singularity-axis), but instead one space direction, the axis direction, is now infinitely long.

If you have a hard time getting to grips with this mixture of time and space, rest assured that physicists have a hard time visualizing it, as well. Luckily, physicists have a language in which the properties of simple black holes can be formulated very precisely – the language of mathematics -, and using this formulation as a guide, it is possible to develop a pretty good intuition about spacetime containing a black hole.
This analogy isn’t perfect. In the analogy, the change-over of space and time happens suddenly, at the boundary. In a more precise formulation, the change-over is more gradual. In a way, the time direction is bent more and more inward as you get closer to the black hole. As the bending is strong enough to prevent any object from moving in any direction but inwards, you cross the horizon.

Also, the black hole is an especially simple specimen. It is spherically symmetric – a so-called Schwarzschild black hole, after Karl Schwarzschild who, in 1915, was the first to write down the equations defining and describing such a black hole; a special solution of Einstein’s equations of general relativity. (However, it took physicists more than forty years to understand the weird spacetime geometry that Schwarzschild’s equations imply!) As has already been mentioned, this type of black hole is eternal – it has always been there, and will always be there. More realistic black holes with a definite beginning (for example those produced by the collapse of a massive star) or eternal black holes which rotate all have a somewhat more complex inside structure.

Apart from these qualifications, the analogy holds, and it does capture an essential aspect of a real black hole’s spacetime geometry – time and space changing places at the horizon, and some fundamental consequences of that exchange.

Under such intense gravitational fields, no life could survive so experiencing time going in directions unknown to life will never be experienced.