What is the actual shape of black holes?

[souriyas]

TL;DR Summary

Black holes have been depicted as two-dimensional and 3-dimensional, so which is it?

When looking at depictions of black holes, we often get illustrations of a two-dimensional space-time where everything spirals into a "hole". The hole then leads to a singularity usually depicted as a funnel shape. Then there are images of black holes shown as spherical with glowing rings swirling around them like in the movie "Interstellar". If black holes are spherical, does it mean that the singularity is the center of that "sphere"? Then what defines the event horizon if the black hole is a sphere?

 

[Ibix]

Black holes are spherical if non-rotating and oblate spheroids if rotating. The glowing ring in Interstellar is outside the hole, and is infalling matter that's heated up to the point that it glows white hot. I believe it's actually just one ring; all the complex structure you see is due to light paths being curved by the very strong gravity, so you see several distorted images of the same ring. Nobel Prize winner Kip Thorne did the modelling for that, so it's as accurate as we know how to make it. I have seen attempts to copy it that aren't so accurate (lookin' at you, Star Trek Strange New Worlds).

Depictions of the interior of a black hole outside textbooks are uniformly horribly wrong. The singularity is not a place inside the hole, it's more like a moment in time in the future of anything entering the hole. That's why it's inescapable - you can't avoid Monday morning either. Attempting to draw this (except in an abstract fashion such as a Kruskal diagram) will never really work.

 

[souriyas]

Black holes are spherical if non-rotating and oblate spheroids if rotating. The glowing ring in Interstellar is outside the hole, and is infalling matter that's heated up to the point that it glows white hot. I believe it's actually just one ring; all the complex structure you see is due to light paths being curved by the very strong gravity, so you see several distorted images of the same ring. Nobel Prize winner Kip Thorne did the modelling for that, so it's as accurate as we know how to make it. I have seen attempts to copy it that aren't so accurate (lookin' at you, Star Trek Strange New Worlds).

Depictions of the interior of a black hole outside textbooks are uniformly horribly wrong. The singularity is not a place inside the hole, it's more like a moment in time in the future of anything entering the hole. That's why it's inescapable - you can't avoid Monday morning either. Attempting to draw this (except in an abstract fashion such as a Kruskal diagram) will never really work.

I'm just trying to imagine, if black holes are spherical like anything that is "spherical" and has mass, does the gravity of black holes act to pull objects toward the center? If I'm understanding you correctly, the singularity is not a place but a moment where space-time is not defined. The confusion is thinking of a black hole as a "hole" but it's spherical or oblate. Technically black holes don't have a surface, correct? If the event horizon defines the boundaries of a black hole, could we think of it as the "surface" of the black hole? Or is the event horizon always flat wherever you are in space-time?

 

[Ibix]

I'm just trying to imagine, if black holes are spherical like anything that is "spherical" and has mass, does the gravity of black holes act to pull objects toward the center?

As long as you are outside it, a black hole works exactly like any other (near-)spherical mass like a star - you fall towards it, you can orbit around it, etc. It's just really, really small for its mass and black. It's only when you are on the inside that your intuition about how gravity behaves will go horribly wrong.

Technically black holes don't have a surface, correct? If the event horizon defines the boundaries of a black hole, could we think of it as the "surface" of the black hole? Or is the event horizon always flat wherever you are in space-time?

The event horizon is the boundary of the black hole - once anything crosses that it can never come back. That's why it's black. It's what I was describing as spherical or an oblate spheroid. But there is nothing at the horizon, no - in fact, nothing can stay at the horizon, only pass through it. You can fall right through it with no issues if the hole is sufficiently large. You're stuck at that point and you'll hit the singularity in fairly short order (about fifteen microseconds for a black hole with the mass of the Sun, if memory serves).

 

[Ibix]

It's only when you are on the inside that your intuition about how gravity behaves will go horribly wrong.

...actually that's a bit of an overstatement. There are some oddities such as no stable orbits below certain altitudes, and with a rotating black hole you don't fall straight down but start to move in the direction of spin of the hole. But it's still a modified version of "you just fall towards the center". Inside is a lot stranger.