What is a Singularity?

Well, we say someone is singular when they are one A single person And not just any individual.

But thats not quite right.

A singularity is more like the answer to a question for which there is no answer.

Here, take this very simple function:

When x is 1 whats, the value of f ( x, ), OK lets substitute 1 over 1 is 1.

Now. What happens when x is zero?

Well, thats easy.

Substitute and The function has no solution, because it doesnt make any sense, because 1 divided by 0 doesnt make any sense unless you use a Riemann sphere in the complex plane which allows for division by zero in some circumstances.

In a way that makes expressions such as this one well-behaved. The point is that these are just constructs:

They dont exist in the real world, they are more like ideas.

See when we built mathematics, we decided the rules and, according to those rules, this equation doesnt make any sense.

It has no answer So whats the problem.

It all goes backs to this guy Einsteins field equations, you can easily derive their exact solution for a single spherical non-rotating mass if your name is Karl Schwarzschild and youre, a genius physicist with a badass mustache, and then you end up with this simple-looking formula.

This c is the speed of light G.

Is the gravitational constant M is the mass of the object and rs is the Schwarzschild radius c and G are constants? Say you have an ball of mass M. If you squeeze it, the mass stays the same, but its volume gets smaller.

If you keep squeezing the ball, it will become tiny, but stay just as massive as before, all the molecules compressed close to each other Until it reaches a critical size and thats the Schwarzschild radius.

It is the radius of a sphere such that, if all the mass of an object were to be compressed within that sphere, the escape velocity from the surface of the sphere would equal the speed of light.

This means that, in order to escape the gravitational pull of the object, whatever tries to get away from, it would have to move faster than the speed of light.

But because the speed of light is constant and nothing can ever go faster, nothing can escape, Including light, It’s essentially a black pit where anything you put in doesnt come back. And thats what we call the congressional budget, I mean a black hole.

Because the speed of light is such a gargantuan number, Its square is f**king gianormous, Which means, unless you have an unbelievably big mass, the Schwarzschild radius is very tiny.

Take the Earth which is pretty massive.

It has a radius of over 6,000 km.

Its Schwarzschild radius is only 8mm I dont think I can even begin to explain the scale of things, it would be like turning this gigantic thing where all of humanity lives, cozily and people take years to travel around by foot Into something the size of a penny.

Lets go back to our Schwarzschild Radius, If the objects radius is less than that, it becomes a black hole, But what happens at the center?

In other words, what happens if the object’s radius IS zero?

This equation defines the shape of spacetime near a spherical mass Now you dont need to understand all of it.

Just have a quick look and see if you can spot the problem.

Congratulations.

You just broke physics By creating a singularity, an imaginary point in spacetime, where all the laws we know dont make any sense.

Now lets make something clear.

The black hole isn’t the singularity – this is the event horizon sort of a beyond this none shall return threshold, that’s the black hole and in the middle, it’s where you divided by zero.

The singularity isnt really a place because in theory it occupies no space and it has infinite density.

Its like the concept of point, in geometry, Its hypothetical, except we have experimentally, discovered black holes, exactly how Einstein and Schwarzschild had predicted, and there is reason to believe that singularities do exists.

There is copious amount of speculation on what might happen at a singularity, including wormholes time, travel and portals to other universes.

We just dont know for sure what happens at a singularity and probably never will

Thank you for being curious.