Schwarzschild radius

The immense, unprecedented gravitational pressure triggers a macroscopic quantum phase transition.

Instead of continuing to fall inward into a singularity, a microscopic, ultra-hard physical shell forms right at the Schwarzschild radius.

A physical shell.

Mm-hmm.

... and special relativity came out, and then you had this physicist called, uh, Schwarzschild come around and play with some of the Einstein equations, and that's where we got the idea of black holes.

And you've probably heard the event horizon called the Schwarzschild radius before.

Yes.

So then based on the math that Schwarzschild did, Einstein and another physicist by the last name of Rosen came in and started playing again with these Schwarzschild, uh, ideas behind general relativity, and they found that it is possible to get a situation, kind of the same situation going on with black holes, but instead of just being this infinite density point in space like a black hole-

These tests provide confidence that general relativity remains valid across the entire range of gravitational strengths, from weak fields where Newton's laws work well to the extreme environments where black holes dominate space and time.

Schwarzschild radius calculations reveal event horizon size for any black hole based solely on its mass.

Karl Schwarzschild discovered this in 1916 by solving Einstein's equations for a perfectly spherical, non-rotating black hole.

The formula is remarkably simple.

Schwarzschild radius equals two times the black hole's mass multiplied by the gravitational constant divided by light speed squared.

For a black hole with 10 solar masses, the radius works out to approximately 30 kilometres.

For a billion solar masses, the radius extends to several billion kilometers, roughly Pluto's distance.

The Schwarzschild radius represents the point of no return, the event horizon.

Is a black hole like a town in size?

So, okay, so the event horizon, the distance from the singularity to the event horizon, that's called the Schwarzschild radius.

And the Schwarzschild radius for something as massive as the sun is three kilometers.

Oh.

That's small, right? That's pretty little.

And this is the size something has to be in order for its escape velocity to be equal to the speed of light.

And a black hole, another definition of a black hole, is something in which the radius of the object is less than the Schwarzschild radius.

Because if the radius is less, then the escape velocity will be even greater.

So, as I say, this was worked out in obscurity in the middle of the eighteenth century, and nobody thought anything much about it.

And so it happened in this case.

Okay, so one question you can ask is, that's all fine.

How big is the Schwarzschild radius for some bunch of objects? Let's try the Sun.

Here, let me start a new piece of paper.

Oh, wow.

If they get close enough, the immense energy they carry, packed into the tiny microscopic volume between them, crosses a critical geometric threshold called the Schwarzschild radius.

A

Schwarzschild radius.

Yes.

The Schwarzschild radius is the ultimate point of no return in general relativity.

It is the specific radius at which any given amount of mass or energy, if squeezed tightly enough inside it, has to form an event horizon.

Because the escape velocity exceeds the speed of light.

So our Bekenstein bound hard drive needs to be roughly 4 by 10 to the power of 80 Planck areas corresponding to 40 billion square meters.

That corresponds to a spherical black hole with a radius around 100 kilometers.

So informationally speaking, you could store the entire observable universe of non-radiation particles on the surface area of a black hole m- the size of Switzerland.

The radius I gave is the Schwarzschild radius, the radius of the event horizon of a non-rotating neutral black hole, again, like Switzerland.

It's directly proportional to its mass.

The mass of 100-kilometer radius black hole would be 30 times that of our sun.

It's a hard drive the size of a picturesque European nation with the mass of the heaviest stars in the universe and with the storage capacity to register every atom in the universe.

Not exactly portable, but you'd never need to defrag again.