## What happens to spacetime inside a black hole? (Intermediate)

What kind of time reversal takes place inside the event horizon of black holes?

Many people are fascinated by the famous "event horizon" of a black hole, the boundary of the region out of which nothing can escape. The mechanism that gives it this property is strange and amazing--it has to do with the idea of causality.

Merlin from the King Arthur legends was supposed to have lived his life backwards--the first thing he experienced was his death and the last was his birth, hence his ability to foretell the future. To us, however, time feels as though it flows only forward. This feeling actually comes from the more general property of causality. In a region like the one here on Earth, you can only remember events that meet 2 criteria: (1) it has to have been in the past, and (2) it has to have happened at a distance no more than what light could have travelled since it happened. The second rule is just the familiar light speed limit. The first is called causality, and it's why you won't meet anyone like Merlin here at home.

Here comes the strange part. General relativity (that same theory supported by so many experiments and needed to make the GPS system work) predicts that, simply by compressing any piece of matter down enough to make a black hole, you create a region where this just isn't true. Inside the event horizon, time and space change places. Therefore the new restrictions go like this: in order for you to remember something, (1) it has to have happened farther from the center of the black hole than where you are now, and (2) if T is the time that it would take light to travel to you from the location of the event, then it happened either no more than T hours ago or T hours into the future.

I recommend thinking about this at least until your head starts to hurt. First of all, note that restriction #1 prevents you from moving away from the center of the black hole, and therefore from going back across the event horizon. Also note that it says "farther", not "at least as far". This means that not only can't you move away from the center, you can't even stand still. Also we see that everyone inside the event horizon is a psychic. This happens because light can travel to you from events in the future, so you can quite literally see them. You can't see anything closer to the center than you are because light can't travel away from the center. If you look away from the center, though, you see two images of everything--one from T hours in the past and one from T hours in the future. For nearby objects, these two images will look just the same, since T will be very small due to the large speed of light. For faraway objects, though, they could be completely different. For instance, if both you and Tolstoy were in a black hole and were separated by 3 light years, you could be watching him start and finish War and Peace at once. At that point in time, he would only be done with half of the book. Of course, you'd want to try sending him a message with the text of the book, to save him some work writing it, but you couldn't--he can't see you at all, since you're closer to the center of the black hole than he is. Pity.

If you think about it for a while, you'll be able to come up with loads of strange situations that can happen inside a black hole--but none of them will be logically inconsistent (such as would be the case if you had been able to send Tolstoy the last chapter of his book before he had written it). There are even more when you consider that realistic astronomical black holes should actually have 2 event horizons--the causality flip discussed above happens at the outer event horizon, and then flips back at the inner event horizon.

#### Sara Slater

Sara is a former Cornell undergraduate and now a physics graduate student at Harvard University, where she works on cosmology and particle physics.

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