I watched a short video, where the guy said that everything that goes inside black hole becomes singularity.
But I can’t comprehend or visualize what singularity actually is?
In: Physics
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.
Latest Answers