This is an example of a question that has been influenced by science fiction literature and movies that seem to warp the truth on things like this for entertainment. But also, the science itself can be confusing. This answer will debunk the incorrect beliefs that we hold and also explain why they are wrong.
So, do black holes actually contain a singularity?
No, black holes in our universe, that is to say the real universe, do not contain singularities.
What is a singularity?
A singularity, when we are talking in terms of black holes, is the term that scientists will use to refer to a non-physical mathematical result of a flawed scientific theory.
They are essentially referring to any errors that can turn up in the theories that we currently hold about things in space that really exist. This means that when we refer to singularities as if they really exist, we are fuelling incorrect assumptions about space, and in this case black holes.
A singularity is also defined as a point in space where there is a mass with an infinite density. This means that the spacetime in that area would have an infinite curvature since mass affects the spacetime and is related to gravity.
Why is it believed by people that black holes contain a singularity?
The reason some people believe that a black hole contains a singularity is because Einstein’s theory of general relativity suggests it is the case. The reason that people believe this due to Einstein’s theory is because it usually yields very good matching experimental results. This is why the theory is trusted by so many scientists.
The issue with people believing this due to Einstein’s theory is that infinities do not exist in the real world. It is generally believed by a lot of scientist that if another person has a theory relies on an infinity, then the theory is too simple to think of anything else.
So, what is the truth, are there any examples?
If you imagine a guitar string where the waves travel along the strong. When you drive this string at its resonant frequency, the prediction is that the string’s vibration will increase over time exponentially, that is to say it will increase more and more rapidly. Even if the string is being plucked gently.
The truth is that the string will vibrate exponentially, but it is only up to a point, not for the rest of time. The guitar string cannot vibrate to pass the sun, moon and stars in the way that the prediction suggests, this would mean it vibrates infinitely, which it does not. The string will actually snap way before it reaches anywhere near the moon.
This means that this model of the theory has definitely reached it limits. The guitar string model is correct when there are only small vibrations, but this is where the model ends. In order to safely avoid the idea of infinity in this string model, there needs to simply be a better theory. In this case, add in that the guitar string will snap at a certain point.
Why does the model have limitations?
Pretty much every single scientific theory has its limitations. A valid and good theory will match experimental results effortlessly. But when you go outside of the limitations of the theory, there will be predictions that are considered complete nonsense.
The ideal situation would be that physicists can create a theory that has absolutely no limitations and works in every experiment. But we obviously do not yet have anything like that. In fact, the best theories in physics are still Einstein’s theory of general relativity as well as quantum field theory.
These are both used for very different reasons, but as long as they are used in the correct setting, they will yield the correct results.
Quantum Field theory
This is a theory that describes, quite accurately, the physics from the size of a human all the way down to smallest particles. But, annoyingly, quantum field theory fails when it comes to the planets and other astronomical bodies. It actually states nothing at all about gravity.
Therefore, using quantum field theory to measure earth’s orbit around the sun will give completely the wrong result.
General Relativity theory
This theory is different in that it accurately predicts the effects of gravitational forces. But, unlike the quantum field theory, general relativity says nothing about atoms or electromagnetism.
In fact, it says nothing about anything on the small scale really. This means that using general relativity theory to predict the electron’s orbit around the nucleus of an atom will simply give you the wrong result.
Do general relativity theory and quantum field theory not get confused?
Luckily, because the two do not actually overlap much at all, the two theories do not get confused. In reality, when you are making calculations on an astronomical scale, you can completely ignore the quantum field theory and only acknowledge the theory of general relativity.
On the other hand, when you are making calculations at a much smaller scale, you can completely ignore the theory of general relativity and only use the theory of quantum field.
Are there any examples of this?
Yes! In fact, when you are describing what the atoms in the sun are doing, you would only use quantum field theory since it is on such a small scale.
But when you are zooming out and looking at what the sun does and how it acts as a whole, you would use strictly general relativity. So, the two theories have their exclusive uses depending on the scale that the scientist is researching and needs calculations for.
Scientists will actually use these two accurate theories in a manner that could be considered a patchwork way. That is to say that we use them interchangeably when we are talking about different scaled particles and astronomical bodies in the universe.
Where do black holes come into this?
Well, getting back to the question at hand. The only way that this patchwork approach to using the theories breaks down is when black holes are considered.
The reason for this is that a black hole is actually an astronomical object that is collapsed into quantum sizes. In other words, it spans the two theories in one lifetime.
If a black hole is collapsed… how is one made?
A black hole is formed when a giant star eventually runs out of the fuel that it uses to balance out the gravity. This means that there are no longer enough atoms to go through nuclear fusion and emit enough energy to cause radiation pressure that counteracts the gravity that pushes inward on the star.
This means that the gravitational pressure on the star has nothing stopping it from collapsing the star.
As we know, the theory of general relativity will predict that the star will collapse into an infinitely small thing with infinite density. This is essentially a prediction based on a theory that worked when the black hole was a star but does not work on the star. We know that this is not the case because such a thing cannot exist in the real universe.
The reality is that you need quantum field theory to work on particles of such a small scale. The only problem with this is that quantum field theory does not account for any gravitational effects, as we mentioned above. And this is the main feature of a black hole!
Conclusion
Because the two theories that we hold as the most recent and most accurate theories to date are not adequate enough to work out a black hole, we do not actually know what is happening in a black hole.
We can make predictions but based on the theories that we have on hand, we cannot know for sure. That is why are lot of theories surround black holes, because we do not know anything for sure.