It’s called null, since light follows null paths, and infinity, since that’s where light “ends up” after traveling infinite distance.

This line is called (future) null infinity. Notice they end up at the (upper) right diagonal line. One nice part about this diagram, sometimes called a Penrose diagram, 2 is that light still travels at 45 degree angles. For clarity, we also drew some coordinate lines based on the old coordinates. It’s kind of weird, but what we did is we compressed the infinite range of time and the infinite range of radii down to a compact area. In fact, it’s weird enough that let’s just sketch a diagram for the Minkowski spacetime in these new coordinates, rather than write out a metric. And we’re going to do a weird kind of coordinate change. Like we did last time, we’re going to mostly ignore the sphere part of the metric (the and parts), and focus on the and parts. (Same spacetime and metric, different coordinates.) However, if we change to spherical spacetime coordinates, the metric in these becomes. To remind you, Minkowski space, the spacetime of special relativity, can be interpreted as a solution of general relativity. It doesn’t seem like there’s anywhere to extend to, like there was before, when we extended into the interior of the black hole.īut it turns out, despite all appearances, we can extend the spacetime further, and discover another universe on the other side of the black hole.īut to understand that we need to talk about a special coordinate change for special relativity. Can we extend the spacetime even further? But a coordinate change let the spacetime make sense inside the black hole as well, for. So, the original presentation of the Schwarzschild metric was problematic, and so it only made sense for, outside the black hole. That’s why we call the sphere at the event horizon, and the whole thing a black hole. Well, except that light can’t escape from inside this radius, due to the extreme bending of spacetime. After a change of coordinates, 1 the weirdness at the Schwarzschild radius goes away, and the spacetime is suddenly well behaved all the way down to. īut last time, we talked about how this apparent singularity is not actually a problem. That means, originally, the metric really only makes sense outside this radius. Īt the Schwarzschild radius,, this metric blows up (i.e., goes to infinity).

The usual form of the metric is, to remind you. The Schwarzschild spacetime, which is the original basis for the theory of black holes, is more complicated than the simple form of the metric would have you think.

Timelike infinity