• The text in italics is copied from that url
• Immediate followed by some comments
In the last paragraph I explain my own opinion.

### Introduction

The article starts with the following sentence.
A gravitational singularity or space-time singularity is a location in space-time where the gravitational field of a celestial body becomes infinite in a way that does not depend on the coordinate system. The quantities used to measure gravitation
The whole issue is what does an infinity physical means. IMO mathematical infinities do not exist. See also Reference 1
The quantities used to measure gravitational field strength are the scalar invariant curvatures of space-time, which includes a measure of the density of matter.
And these densities can never be infinite
Since such quantities become infinite within the singularity, the laws of normal space-time could not exist.
Quantities become infinite based on certain equations. When the calculations reach infinite values the equations are wrong. The problem is most probably in the constraints.
A type of singularity predicted by general relativity is inside a black hole: any star collapsing beyond a certain point (the Schwarzschild radius) would form a black hole, inside which a singularity (covered by an event horizon) would be formed.
From a physical point of view it is not spectacular that a star collapses and forms (what we call) a Black Hole because light cannot escape from their surface. The issue is that their behaviour general speaking is identical as a normal heavy star except if observations indicate other wise. That means you do not need the concept of event horizon and infinity.
According to modern general relativity, the initial state of the universe, at the beginning of the Big Bang, was a singularity.
That may be true, but if you do not explain what a singularity physical means the sentence explains nothing

### 1. Interpretation

Many theories in physics have mathematical singularities of one kind or another.
Than these theories do not describe the physical reality correct.
Equations for these physical theories predict that the ball of mass of some quantity becomes infinite or increases without limit.
Same issue.
Some theories, such as the theory of loop quantum gravity suggest that singularities may not exist.
That is a correct assumption, but that does not mean that quantum gravity theory is correct.
The idea can be stated in the form that due to quantum gravity effects, there is a minimum distance beyond which the force of gravity no longer continues to increase as the distance between the masses becomes shorter, or alternatively that interpenetrating particle waves mask gravitational effects that would be felt at a distance.
This is a very complex sentence. The issue is: which physical effect do you try to explain. The physics involved in the behaviour of a binary Black Hole pair is completely different as the physical process that describes how the Black Hole formed in the first place.

### 2 Types

There are different types of singularities, each with different physical features which have characteristics relevant to the theories in which they originally emerged from, such as the different shape of the singularities, conical and curved.
When there are singularities and when these singularities have different shapes than you should describe what that physical means.

### 2.1. Conical

A conical singularity occurs when there is a point where the limit of every diffeomorphism invariant quantity is finite, in which case space-time is not smooth at the point of the limit itself.

### 2.2. Curvature

Solutions to the equations of general relativity or another theory of gravity (such as supergravity) often result in encountering points where the metric blows up to infinity.
Than certain tests are required to prevent this.
However, many of these points are completely regular, and the infinities are merely a result of using an inappropriate coordinate system at this point.
Something in this sentence is wrong..
If what you describe (in the physical world) as regular than if using mathematics the results should match and not depent on the coordinate system. It also should not result in infinities. This implies that the mathematics used is incomplete i.e. requires additional constraints.
More generally, a space-time is considered singular if it is geodesically incomplete, meaning that there are freely-falling particles whose motion cannot be determined beyond a finite time, being after the point of reaching the singularity.
To describe the physical behaviour of an elementery particle outside the Sun and inside the sun is completely different.

### Reflection 1

In physical sense, mathematical infities do not exist.
When you consider Newton's Law (and all the laws which are similar) the r in that law defines the distance between the center of two objects. That distance can never be zero. As such there are no infinities in Newton's Law. To prevent such problems to happen you should implement a test in your simulation that the distance between the objects should also be larger than a minimum distance rmin. When the distance becomes less than dmin you declare a collision between the objects.
More or less the same is involved in the behaviour of Black Hole's. A Black Hole is a collapsed normal star. That means the internal density is much higher than for a similar sun like star with the same mass. To prevent infinties to happen simple test should be included based on a minimum radius of the black hole.

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Created: 1 February 2016

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