One of the most popular questions asked about relativity concerns what would happen as an object approaches the speed of light. If it were moving fast enough, would it become a black hole? The same question could be asked another way: are you a black hole? The answer to the second question is obviously no. So is the answer to the first question. Confused?
The basic argument is as an object approaches the speed of light from our perspective, three things happen. It’s time appears to slow down (time dilation), it appears to get shorter along its direction of travel (length contraction), and its mass appears to increase (relativistic mass).
These are all consequences of relativity and the fact that light has the same speed in all frames of reference. Relativity also says that a large enough mass in a small enough volume becomes a black hole. So it seems reasonable that an object near the speed of light should become a black hole.
If that were true, you must be a black hole.
Here’s why: the Universe is expanding. It’s not just that galaxies are racing away from us, space itself is expanding. This means that the more distant an object is from us, the faster it is moving away from us. There are distant galaxies moving away from us at nearly the speed of light. That means we are moving away from them at nearly light speed, so we should appear to be a black hole to them.
But the thing about black holes is that you either are one or aren’t one. A black hole’s event horizon must exist in all frames of reference. So if you aren’t a black hole in your frame of reference (and you’re not) then you’re not a black hole in any frame of reference. So a fast moving object does not become a black hole.
So what gives? It turns out the original argument is flawed. It’s true that an object’s relativistic mass does increase with speed. This means they are increasingly difficult to push, making it impossible for them to reach the speed of light. But everything is relative. From our perspective we have to keep pushing harder. From the object’s perspective our pushes keep getting smaller. As far as the object is concerned it’s mass hasn’t changed. So naturally it doesn’t become a black hole.
Just as you aren’t a black hole because you’re speeding away from distant galaxies. An object speeding away from us doesn’t become a black hole.