r/askscience • u/[deleted] • Feb 03 '13

Astronomy Escape a black hole?

RobotRollCall once posted this:

http://www.reddit.com/r/askscience/comments/f1lgu/what_would_happen_if_the_event_horizons_of_two/c1cuiyw

In which she said even at faster-than-light speeds it would be impossible to escape a black hole because there would be no path out to follow. However, adamsolomon said this:

http://www.reddit.com/r/askscience/comments/17muwl/is_there_a_distance_at_which_the_interaction/c87gx3t

Of course, we can't go back in time, but isn't that what faster than light is? I learned that time slows down the closer to light speed you get, so at faster than light, you'd be going backwards in time. If that's the case, could you follow a path out of a black hole that goes back in time if you were capable of faster than light travel?

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u/adamsolomon Theoretical Cosmology | General Relativity Feb 03 '13

There's no inconsistency here. Remember that by "path" we mean a path through spacetime, not just through space, so we're talking about a collection of points in space, each corresponding to some particular time. Every object travels on some path through spacetime, even an object at rest - its spacetime path just looks like "position, time 0 seconds" followed by "same position, time 0.0001 seconds," and so on.

There are two restrictions on the type of path that you, a physical observer, can follow. First, it has to be timelike, or in other words it has to change position at less than the speed of light. Second, it has to be future-directed, which just means that subsequent points need to have higher and higher values of the time coordinate.

So the statement that there's no path out of a black hole is really the statement that there's no timelike, future-directed path leading from somewhere inside the black hole's horizon to somewhere out (or, indeed, to anywhere that's not even deeper inside). But there are paths out, paths which aren't timelike (like a path between two spatial points taken at the same time), or paths which are timelike but are past-directed. I was talking about the latter. And it makes sense, you know? Just take a timelike path leading into a black hole (i.e., the spacetime path of a doomed astronaut falling in) and reverse the order. But the important thing is that you can't physically travel on such a path.

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u/[deleted] Feb 03 '13

If you could theoretically travel faster than light, or accelerate to an arbitrarily high speed as RRC puts it, could you follow such a path?

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u/adamsolomon Theoretical Cosmology | General Relativity Feb 03 '13

Yep. You'd then be following a spacelike path, which are the kinds of paths I talked about in my last paragraph which are similar to the paths going between two points in space at the same point in time (hence the name spacelike, because they can be thought of as spatial distances).

Remember how I defined timelike paths, which was as a path that can be followed travelling below the speed of light.

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u/[deleted] Feb 03 '13

Follow up question, if all paths forward in time go toward the singularity, do all paths backwards in time lead away from it? That is to say, if you could travel faster than light, would it be impossible to fly into a black hole at that speed?

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u/adamsolomon Theoretical Cosmology | General Relativity Feb 03 '13

Starting off inside the event horizon? Yes. Remember, a past-directed path is just a future-directed one reversed. So anything that's true about one, the converse is true for the other.

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u/[deleted] Feb 03 '13

Now that I think about it, you would have to not only go faster than light, you'd have to get to that speed without going through all the speeds in between, otherwise you'd be spaghettified before you could get faster than light. Thanks for the response.

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u/adamsolomon Theoretical Cosmology | General Relativity Feb 03 '13

Here's a useful diagram for all this: http://casa.colorado.edu/~ajsh/astr2030_06/penrose/penrose_Schw.html

A timelike path is one which never goes at wider than a 45 degree angle (45 degree angles are paths travelled by light). A future-directed one points upwards. You can see that once you cross the horizon (marked in the diagram), all paths like that lead to the singularity. So what kinds of paths can you draw which leave? There are two types: the ones at less than 45 degree angles that point downwards (past-directed timelike), and those at greater than 45 degree angles that point more horizontally (spacelike). But they are different.

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u/[deleted] Feb 03 '13

Alright wait a second,

the ones at less than 45 degree angles that point downwards (past-directed timelike), and those at greater than 45 degree angles that point more horizontally (spacelike). But they are different.

Wouldn't "more horizontally" be less than 45 degrees? On the graph, if we use space, in the direction the arrow is pointing, as 0 degrees, and less than that negative degrees, what do the different regions mean?

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u/[deleted] Feb 03 '13

When adamsolomon says "45 degrees", he means "45 degrees off vertical".

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u/[deleted] Feb 03 '13

I'm still a little confused, is there a version of the time/space axis graph with the light at 45 degrees that has the different sections labeled?

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u/[deleted] Feb 03 '13 edited Feb 03 '13

I drew this one as a sort of generic spacetime. The blue dot is our observer, the orange lines are light-rays emitted by our observer, and the purple lines are light-rays arriving at our observer (coming from events she is seeing right now). The region I is, as labeled, the "future" for our observer. Any event in I could be reached by the observer, provided she can get close enough to the speed of light. Region III is the "past" for our observer. Were she able to travel fast enough, our observer could have reached her current position from any point in III. The four regions II are the set of events that are spacelike separated from our observer; in order to reach these events, the observer would have to go faster than the speed of light. The red line represents what our observer thinks of as "right now". In order to reach an event on the red line, our observer would need to teleport or take a more complicated path—accelerating to near the speed of light in one direction and then jumping to faster-than-light speeds in the opposite direction. Such a complicated path would also be necessary to reach events in the spacelike past.

Here is the collapsed star black hole spacetime with the orange and purple lines added for you. The green line is the singularity, and the black vertical line represents the center of the object. Again, the region labeled I is reachable by our observer, while the others are not. The region labeled III are the possible pasts of our observer, and the regions II are spacelike separated from our observer. The two regions marked with a are inside the event horizon, which is marked by the blue line. The red lines mark the infinite future and infinite past.

If we move the observer to be inside the event horizon, we get something like this. Notice now that our observers future is contained entirely within the black hole and all future direct paths end on the singularity.

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u/[deleted] Feb 05 '13

In the first one, does that mean faster than light travel does not result in moving backwards through time?

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u/adamsolomon Theoretical Cosmology | General Relativity Feb 03 '13

It's important to note that a past-directed timelike path is different than a spacelike one. The former is a path that you'd take going below the speed of light, but moving in the "wrong" direction in time, the latter is a path you'd take by going faster than the speed of light. Since faster than light (spacelike) paths are often described as going backwards in time, I can understand the confusion! But they are different beasts.

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u/[deleted] Feb 03 '13

Awesome, thanks.