It’s the point where our understanding of physics breaks down. If you follow the math, all the mass falling into the black hole ends up in the center with size zero. A true point with no radius. This seems really weird, but we have no idea why it would not do that. So a speculation is that there is more going on, but we haven’t developed the theories to explain it yet. Since nothing inside a black hole can communicate with something outside a black hole we have no way of finding out what happens.

In simplest terms, gravitational singularities happen when our mathematical models for gravity have a “divide by 0” in them. It is where our models for gravity break down.

The main place these occur is at the centre of black holes. But as “inside” a black hole is already a bit of a messy idea, it isn’t that big of a problem that our models break down at the centre of black holes.

The main thing that happens inside a black hole is you get really intense gravitational gradients, where the bottom of something is being pulled down much faster than the top, so things get stretched. Which is generally bad. Plus you get a lot of stuff being pulled in, so things are really hot and crowded/

A singularity is when a mathematical function aproaches infinity. Like a division by zero(if you plot it on a graph – f(x)= 1/x), if you aproach it from the positive number side it aproaches infinity, if you aproach it from the negative side it goes to negative infinity. At exactly zero you have a singularity.

Its not clear if this is a thing that can even exist in our real world. The border to a black hole is not a singularity uts te event horizon, the border that we can never see behind. The actual singularity of a black hole would be a point in the center, but we dont know if thats actualy there. Its just that the graph you plot to show spacetime has a mathematical sungularity at that point if you use Einsteins formula for it.

What this most likeley means is just that te math is wrong.

A singularity is a rules violation in math. Sometimes when the math describes physics, that results in a physical limit, like the coldest possible temperature or the speed of light.

The black hole singularity occurs when you look at the speed to orbit a star. The more massive the star, the faster you have to go. there reaches a point where too much mass means you can’t orbit the star without exceeding the speed of light. Our mathematical representation of orbital mechanics fails, and no force can get your spaceship back.

Perhaps this is a bug in our math. We had some math problems with the speed of airplanes, but we invented some new hypersonic equations to represent what’s happening at those high speeds. However, nobody in the physics community thinks the speed of light isn’t a real, actual, you can’t go faster, kind of limit.

A singularity is where a quantity in an expression (e.g., the curvature of spacetime in the solutions to the equations of general relativity) goes off to infinity, usually as a result of division by 0. It’s a point where the maths breaks down and the equation can’t meaningfully describe what’s going on physically anymore.

It’s important to note that the presence of singularities in the *maths* of GR does not mean real physical reality has singularities inside black holes. Actually, the fact that *the equations* (e.g., in the Schwarzchild metric) have singularities in them is a suggestion to many that general relativity, for all its resounding successes, is still not the complete picture. Usually when an equation has division by zero, it’s a sign something is missing from your model.

Singularities are the reason that GR is in irreconcilable conflict with quantum mechanics, and either both are wrong and we need a paradigm shift (exotic stuff like string theories), or we’ll find a unified theory of quantum gravity that unifies the two.

We don’t *know* that black holes have singularities with infinite gravity or infinite density. Our *models* of black holes (the equations of GR, and the solutions to GR we derive like the Schwarzchild metric—the Kerr metric is a little more complicated b/c rotating black holes don’t necessarily have a point-like singularity) have singularities in them. But our models are incomplete, and the mere presence of a singularity in the model is highly suggestive of the common interpretation that at that point, the model breaks down and fails to describe what’s actually going on physically.

Nobody’s ever jumped inside a black hole and taken measurements of gravity or density or spacetime curvature. Rather, our models *predict* there’s a singularity, a terminus of spacetime at the center of black holes.

And in fact, some argue that we’re interpreting it wrong. The Penrose Singularity theorem has widely been interpreted to prove that the interior spacetime region of any black hole surrounded by an event horizon must be geodesically incomplete, i.e., it must contain a singularity. But Roy Kerr (the same guy after whom the Kerr metric for rotating black holes is named) argues that’s a faulty conclusion. He argues that just because the affine parameter is bounded doesn’t mean there has to be singularities.

A singularity is the equivalent of old maps’ Here Be Dragons. Simply: the math people can’t figure it out yet, and they can’t make sense of the math at a certain point. Then they invent this nice name to hide the fact that they know nothing about it. So there may be pink elephants in singularities that we simply are too stupid to figure out.

These things happen in math all the time. For example, people just know taking the square root of a negative number doesn’t make sense, until someone figured it out

One day we may figure out the singularity inside a black hole, but right now nobody really know whats there.

A “singularity” is a generalization of an “asymptote”. It refers to a point on a mathematical object (like a function or relation) where the object is not defined or not “well behaved” (meaning that the function has some kind of inconvenient property at that point which makes it difficult to work with).

Unlike an asymptote, a singularity does NOT have to diverge to infinity. For example, all of the following are singularities:

* The infinite oscillation between -1 and +1 at x = 0 of [the function sin(1/x)](https://www.desmos.com/calculator/szerwuui6a)

* The sharp corner at x = 0 of [the function |x|](https://www.desmos.com/calculator/jb20y0vudl), which means the function is not differentiable at that point (i.e. sharp corners do not have a “slope” that can be measured).

* The jump continuities of a [step/floor function](https://www.desmos.com/calculator/fjrvuxujnq) – not only because the function is not continuous at those points, but also because the limit from the left at those points converge to a different value than the limit from the right.

And of course, the asymptote at x = 0 for [the function 1/x](https://www.desmos.com/calculator/nifgagu35i) is also a singularity.

Note that I have given examples for single dimensional functions, but singularities can also be found on complex-valued functions and multidimensional functions. For example, a [complex-valued Gamma Function](https://www.shadertoy.com/view/sljSzD) has singularities along the real axis at the points of each negative integer.

A singularity is a point where things don’t behave the way they normally do, usually because some quantity goes to infinity (as many people have pointed out), but sometimes because something goes to zero.

For instance, a singularity of a vector field is a point where its value is zero. The reason is that [if the vector field is continuous and] you were to zoom in on a point where the value of the vector field is not zero, you’ll see essentially all vectors point in the same direction. But if you zoom in on a singularity, all sorts of weird things might happen (vectors all point to the singularity, or away from it, or they point to it in some parts and away from it in others, or the vectors circle around the singularity…).

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