# Forming Black Holes

I've read a play (The Square Root of A Sonnet) about the physicist who proposed the Chandrasekhar limit, Subramanyan Chandrasekhar, and had a doubt regarding an argument that was put forward regarding the formation of black holes. I wanted to write an article about it but wanted to ensure that my understanding about the entire topic was right. Do inform me of any further details I may have missed. This is more or less an concept-understanding attempt and I hope it's well-received by the site.

Black Hole Formation:-

A Black Hole is formed when the escape velocity of any object is greater than the speed of light. This causes an immense gravitational pull whereby the object would begin to collapse in on itself. As it does, the objects particles come closer and closer (increasing the density to an enormous amount simultaneously).

But in the process of the particles going close to one another, their position is becoming more and more well defined due to which their velocity is becoming more uncertain (as per the founding principle in Quantum Mechanics-Heisenberg's Uncertainty Principle which states

$$\Delta x \Delta p =\frac{\hbar}{2}$$

). Hence by one of the pillars in modern physics, the particles begin to vibrate in an extreme speed. Due to this, the object begins to move outward (i.e.expands instead of collapsing)

However, their speed is only limited by another pillar of modern physics-Special relativity which shows that the maximum speed any object can achieve is the speed of light. Therefore, by the laws of Special Relativity, every particle attains a speed close to the speed of light cannot move any faster. Therefore, the particles continue to collapse (since the gravitational pull is far stronger) and forms a black hole - A structure formed by the laws of Quantum Mechanics and Special Relativity but seemingly defies both.

Is this all correct or have I missed something? Moreover, is there anything further I could add?

I think there are two key problems with your text:

1. The basic modelling of black holes is entirely classical, depending only on general relativity, which is a classical theory. There is no need to invoke quantum mechanics to explain the existence of black holes. Although there are undoubtedly QM effects close to the horizon of a black hole, the interaction between GR and QM is not completely understood (otherwise we would have a theory of quantum gravity already).

2. The uncertainty in position/momentum arising from Heisenberg's Uncertainty Principle is not due to a "vibration", and does not result in a "pressure".

• 1. I see your point but a black hole is a structure that “seemingly defies both laws” of QM and SR right? 2. I didn’t say ‘pressure’ but there is a constraint on position bringing about a larger velocity (till it meets its Limit by SR)? Feb 14, 2020 at 1:03

Depends - on certain (very low) level it sounds about right.

On different level it is not so easy. If you have Earth instead of black hole, then object with velocity less then escape velocity can still go further and further away from the Earth - the distance it can reach is just bounded. In case of black hole, no matter the (subluminal) velocity, the object will always move toward the center. That is just one example, where the traditional concepts and intuition are dramatically different, or straight out fail.

The main thing about black holes is, that the relativistic effects of gravitation are extreme, so nonrelativistic ideas (like concept of escape velocity, which I am not even sure make any sense for a black hole) do not really apply for them and if you wish to understand them, you need to study general relativity.

Also, from your description one cannot know, if such process could ever happen. You assume there is already strong enough gravitational field to overcome any pressure matter could ever exert. But during collapse the gravitational pull on outer and pressure are strongly coupled together. It could be, that the pressure due to Heisenberg's Uncertainty Principle would increase more rapidly than gravitational pull as body collapses -> as it happens for bodies of small enough masses. Then, your supposed situation of superluminal escape velocity could be never reached and no black hole could be ever formed by this process.

• From the conversation in the play,I think Subramanyan Chandrasekhar took everything into account( including The HUP) before calculating the limit. However I don’t really see the use of your first 2 paragraphs. Feb 14, 2020 at 1:01