At the event horizon of a black hole, time and the spatial direction toward the center exchange places. The direction inside the black hole from the event horizon to the the singularity in the center is the direction in time.
Assume a symmetrical non-rotating black hole and also assume that things can actually fall to the black hole. Consider that over 10 billion years a number of relatively small objects fall in. Finally, at the end, a number of larger objects also fall in that are big enough to increase the size of the event horizon.
Now let's look what's happening inside. The distance from the event horizon to the center is a time coordinate. Therefore, inside a symmetrical black hole, does the sphere of the event horizon represent the same moment of time? If so, then all things that have been falling in over 10 billion years appear all at once on the inside at the same moment that the sphere of the event horizon represents. Is this correct?
Finally, when the larger objects fall in and increase the size of the event horizon, on the inside, a larger radius would represent an earlier time than a smaller radius. Correct? If so, the larger things that fell in at the very end appear on the inside before everything else that's been falling in over 10 billion years. Is this the proper understanding?
In fact, if a black hole has been growing over time gradually increasing in size by sucking the external matter in, on the inside this process would appear happening in reverse, because time inside goes from a larger to smaller radius of the event horizon. Is this correct?
And if it is, then would this not violate causality? For example, consider that a large asteroid was supposed to fall in at the very end, but got hit by another asteroid and both avoided being sucked into the black hole. However, on the inside, this asteroid falls in "before" everything else and therefore is already there when everything else falls in.
Best Answer
Time and space don't swap places inside a black hole.
In order to describe what happens in spacetime we have to attach labels to spacetime points, and these labels are our coordinate system. That is, we choose some coordinates $t$, $r$, $\theta$ and $\phi$ then we can label points in spacetime by their coordinates $(t, r, \theta, \phi)$.
But there are lots of ways to form a coordinate system. The usual one for describing the exterior of black holes are called the Schwarzschild coordinates and these correspond to the physical measurements made by an observer an infinite distance from the black hole. So the Schwarzschild $t$ coordinate is the time measured on the Schwarzschild observer's clock. However there are lots of other ways to make a coordinate system. Gullstrand-Painlevé coordinates are superficially similar but now $t$ is the time measured on a clock held by an observer falling freely into the black hole. Or Kruskal-Szekeres coordinates use abstract coordinates that don't correspond to anything measured by an observer.
The point of all this is that the coordinates are not spacetime - they are just labels we attach to spacetime. What happens inside an event horizon is not that time and space swap places but rather that the labels we call Schwarzschild coordinates behave oddly inside a black hole. This is an important distinction. If we use the Kruskal-Szekeres coordinates instead then we have a spacelike coordinate $u$ and a timelike coordinate $v$ and these do not swap places inside the black hole.
It is fairly easy to see why the Schwarzschild coordinates are not a good description for the interior of a black hole. If we drop something into a black hole and start timing its fall we discover that the object takes an infinite time to even reach the event horizon. That is, no matter how long we time for the falling object never reaches the horizon. In fact for Schwarzschild observers black holes don't exist because any black hole will take an infinite time to form. So by using Schwarzschild coordinates to label the interior of a black hole we are labelling something that doesn't exist. Is it then any wonder that the behaviour of our labels, our coordinate system, inside the black hole is bizarre?
Where things get confusing is that even though in the Schwarzschild coordinates black holes can never form this does not mean they don't exist. For example if you're standing on the surface of a collapsing star then in your rest frame not only does the black hole form in a finite time, but you will fall through the event horizon and to your fatal encounter with the singularity in a finite time. The Schwarzschild $t$ coordinate only covers your trajectory up to the formation of the horizon, but your trajectory carries on past the point where the Schwarzschild $t$ coordinate reaches infinity. But once again let me emphasise that this is just a failing of the Schwarzschild coordinate system. Time carries on for you as normal - it's just just that the Schwarzschild coordinates are not a good way to label time in those circumstances.