Today I want to talk about the history of black holes. But before I get to this, let

me mention that all my videos have captions. You turn them on by clicking on “CC” in

the YouTube toolbar. You can also find transcripts of my videos on my blog at backreaction dot

blogspot dot com

Now about the black holes. The possibility that gravity can become so strong that it

traps light appears already in Newtonian gravity, but black holes were not really discussed

by scientists until it turned out that they are a consequence of Einstein’s theory of

general relativity. General Relativity is a set of equations for the curvature of space

and time, called Einstein’s field equations. And black holes are one of the possible solution

to Einstein’s equations. This was first realized by Karl Schwarzschild in 1916. For

this reason, black holes are also sometimes called the “Schwarzschild solution”.

Schwarzschild of course was not actually looking for black holes. He was just trying to understand

what Einstein’s theory would say about the curvature of space-time outside an object

that is to good precision spherically symmetric, like, say, our sun or planet earth. Now, outside

these objects, there is approximately no matter, which is good, because in this case the equations

become particularly simple and Schwarzschild was able to solve them.

What happens in Schwarzschild’s solution is the following. As I said, this solution

only describes the outside of some distribution of matter. But you can ask then, what happens

on the surface of that distribution of matter if you compress the matter more and more,

that is, you keep the mass fixed but shrink the radius. Well, it turns out that there

is a certain radius, at which light can no longer escape from the surface of the object,

and also not from any location inside this surface. This dividing surface is what we

now call the black hole horizon. It’s a sphere whose radius is now called the Schwarzschild

radius.

Where the black hole horizon is depends on the mass of the object, so every mass has

its own Schwarzschild radius, and if you could compress the mass to below that radius, it

would keep collapsing to a point and you’d make a black hole. But for most stellar objects,

their actual radius is much larger than the Schwarzschild radius, so they do not have

a horizon, because inside of the matter one has to use a different solution to Einstein’s

equations. The Schwarzschild radius of the sun, for example, is a few miles,

whereas the actual radius of the sun is some hundred-thousand miles. The Schwarzschild

radius of planet Earth is merely a few millimeters. Now, it turns out that in Schwarzschild’s

original solution, there is a quantity that goes to infinity as you approach the horizon.

For this reason, physicists originally thought that the Schwarzschild solution makes no physical

sense. However, it turns out that there is nothing physically wrong with that. If you

look at any quantity that you can actually measure as you approach a black hole, none

of them becomes infinitely large. In particular, the curvature just goes with the inverse of

the square of the mass. I explained this in an earlier video. And so, physicists concluded,

this infinity at the black hole horizon is a mathematical artifact and, indeed, it can

be easily removed.

With that clarified, physicists accepted that there is nothing mathematically wrong with

black holes, but then they argued that black holes would not occur in nature because there

is no way to make them. The idea was that, since the Schwarzschild solution is perfectly

spherically symmetric, the conditions that are necessary to make a black hole would just

never happen.

But this too turned out to be wrong. Indeed, it was proved by Stephen Hawking and Roger

Penrose in the 1960s that the very opposite is the case. Black holes are what you generally

get in Einstein’s theory if you have a sufficient amount of matter that just collapses because

it cannot build up sufficient pressure. And so, if a star runs out of nuclear fuel and

has no new way to create pressure, a black hole will be the outcome. In contrast to what

physicists thought previously, black holes are hard to avoid, not hard to make.

So this was the situation in the 1970s. Black holes had turned from mathematically wrong,

to mathematically correct but non-physical, to a real possibility. But there was at the

time no way to actually observe a black hole. That’s because back then the main mode of

astrophysical observation was using light. And black holes are defined by the very property

that they do not emit light.

However, there are other ways of observing black holes. Most importantly, black holes

influence the motion of stars in their vicinity, and the other stars are observable. From this

one can infer the mass of the object that the stars orbit around and one can put a limit

on the radius. Black holes also swallow material in their vicinity, and from the way that they

swallow it, one can tell that the object has no hard surface. The first convincing observations

that our own galaxy contains a black hole came in the late 1990s. About ten years later,

there were so many observations that could only be explained by the existence of black

holes that today basically no one who understands the science doubts black holes exist.

What makes this story interesting to me is how essential it was that Penrose and Hawking

understood the mathematics of Einstein’s theory and could formally prove that black

holes should exist. It was only because of this that black holes were taken seriously

at all. Without that, maybe we’d never have looked for them to begin with. A friend of

mine thinks that Penrose deserves a NobelPrize for his contribution to the discovery of black

holes. And I think that’s right.

Thanks for watching, see you next week.