Black Hole Geometry Will Warp Your Brain | Janna Levin
About The Episode
Black holes can be bigger on the inside than they are on the outside. Astrophysicist Janna Levin explains how this is possible, and what that means about how black holes work.
For more, check out the extended interviewwith Janna Levin.
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HAKEEM: They're bigger on the inside than they are on the outside.
JANNA: Oh, yeah.
HAKEEM: So I've never actually solved the geometry inside of a black hole.
JANNA: Yeah, yeah, they can be bigger.
HAKEEM: So, how does that come about?
JANNA: Yeah. So black holes being bigger on the inside than the outside. The way I think about it, let's say you draw a circle, okay? And we all are used to drawing a straight line to the center of that circle. So, that's flat. And I know exactly how much area is contained in that flat geometry, but if it's curved, if I pull, if it's a little net webbing and I pull it like a horn, like a trumpet, now there's a lot more area until you get to the center because of the curvature. So curved things can hide... That's a little misleading because I had to bend it into a third dimension, but yes.
HAKEEM: Into another dimension. So that reminds me of the way they used to determine the areas of Euclidean figures with triangles inside of it, so you can get the area of a circle, but.
JANNA: Yeah. Everything we believe about areas and volumes inscribed with boundaries, yeah.
HAKEEM: So if I put a rectangle, a triangle inside of a black hole, the three angles don't sum to 180.
JANNA: They do not, and so it's non-Euclidean geometry. It's not flat geometry. And that's exactly it, that the space time is curved. Now, I can't really do that with the black hole because I'd have to visualize it in curving in a different dimension. It's very hard to do. You don't have to do the curving. And we all see these pictures of these funnels that are meant to indicate black holes. And what that really is, is an embedding diagram. It's not that the black hole, this is an actual direction in space which it bends into. That's not it, but it just helps you visualize. They're called embedding diagrams because they help you visualize the curvature as best that we can in our limitations of our visualizations.
HAKEEM: Our 3D limit.
JANNA: Our D minds.
HAKEEM: Yes, oh, boy.
JANNA: But we do know, everything we believe about the volume in inside of sphere is based on Euclidean geometry.
HAKEEM: That's right.
JANNA: And it's not Euclidean in there. And so they can be very big on the inside. You can have all kinds of strange things you can add to the interior of black holes just to noodle around. We don't think nature does that when it collapses stars. But if I'm just playing games with general relativity, I mean, I can put all kinds of crazy things on the interior of a black hole.
HAKEEM: Wow.