Black holes - bigger on the inside
Guess what: black holes are bigger inside than they look - and they get bigger as they get older!
For example, take the big black hole in the center of our galaxy, called Sagittarius A*. It's about 2 million kilometers across. That's pretty big - but the orbit of Mercury is 60 times bigger. This black hole is old, roughly a billion years old. And here's the cool part: it's been growing on the inside
all this time!
How is this possible? Well, since spacetime is severely warped in a black hole, its volume can be bigger than you'd guess from outside. And its volume can change. Since we understand general relativity quite well, we can calculate how this works! But nobody thought of doing it until last year, when Marios Christodoulou and my friend Carlo Rovelli did it.
How big is the black hole at the center of our galaxy? On the inside
, it can hold a million solar systems! Its volume is about 10^34 cubic kilometers! And it's growing at a rate of about 10^25 cubic kilometers per year!
Or suppose you have an ordinary star that turns into a black hole. This black hole will last a long
time before it evaporates due to Hawking radiation. Christodolou and Rovelli estimate how big its volume will get before this happens. And it gets really big
- bigger than the current-day observable universe!
Before you get too excited, remember: people falling into the black hole will not have time to do anything fun inside. They will hit the singularity in a short time. Very very roughly speaking, the problem is not the shortage of space
inside the black hole, it's the shortage of time
If you fall into the black hole at the center of our galaxy, it will be about 1 minute, at most, before you hit the singularity. You will not get to see most of the space inside the black hole! The singularity is not in the 'middle' of the black hole - it's in your future
. You will hit it before you can reach the 'middle'. So, you will only get to see part of the 'edge regions' inside the black hole.
The 'middle regions' can only be seen by people who fell in much earlier. And they can't see the 'edge', where you are!
And now for the serious part.
The hard part of this problem is defining
the volume inside a black hole.
If you choose a moment in time, the black hole's event horizon at that moment is a sphere. There are infinitely many ways to extend this sphere to a solid ball. In other words: there are many ways to choose a slice of space inside
the black hole whose boundary is your chosen sphere.
The slice can bend forwards in time, or backwards in time. We can choose a wiggly slice or a smooth one. Each slice has its own volume.
How do you choose one, so you can calculate its volume? Christodoulou and Rovelli choose the one with the largest
volume. This may sound like it's cheating. But it's not.
Think of a simpler problem one dimension down. You have a loop of wire. You ask me: "What's the area of the surface whose boundary is this loop?"
I say: "That's a meaningless question! Which
surface? There are lots!"
You say: "Pick the best one!"
So, it's up to me. I take some soapy water and make a soap film whose boundary is that loop. That's the surface I use. If the loop of wire is not too crazy in its shape, this surface is uniquely defined. In some sense it's the "least wiggly" surface I could choose.
This surface minimizes
the area. A more wiggly surface would have more
Christodoulou and Rovelli are doing the same thing. But spacetime is different than space! If you choose a wiggly 3-dimensional spatial surface in spacetime, it will have less
volume than a flatter surface with the same boundary!
So, the way to pick the flattest, nicest spatial surface inside our black hole is to pick the one that maximizes
If you tried to minimize
the volume, you could get it as close to zero as you wanted. And this would have nothing to do with black holes! This would be true even in your living room.Puzzle:
Here's the paper:
• Marios Christodoulou and Carlo Rovelli, How big is a black hole?, http://arxiv.org/abs/1411.2854