Theory of relativity as basis for Black hole.

Einstein's Theory of relativity is definitely one of those few theories in the history of physics, that changed the way we see things. It revolutionized the cosmology in such a way that many physicists who are struggling in their respective lines of research produced some shockingly interesting results.

Black holes is one such shocking yet interesting result....

So, what is a black hole?

Well, there are a lot of definitions, and in the simple possible way: A Black hole is a region in space-time with such an immense gravitational pull towards its center that even light cannot escape out of it.

How is Einstein's 'Theory of relativity' responsible for its formation?

Black hole is a subject where its formation is almost entirely based on theoretical evidences rather than physical evidences(strong). All these theoretical proofs are in fact been implied from the Theory of relativity.
To get some idea about its formation and stuff, we must know the life cycle of a star as a prerequisite.

A star takes birth when large amount of nearby gaseous particles(mostly hydrogen) attract towards each other and get squeezed.
In this process of contraction, particles collide with each other to produce large quantities of heat energy. This heat in fact is responsible for the star to shine brightly. The heat thus produced would be so immense that, the particles when they come closer will no longer collide but coalesce, and forms higher elements like helium, Lithium, Berilium...along with some amount of heat. Heat that got released in this process, creates high pressure between the particles and tries to drive them away, opposing the contraction process. The more the star tends to contract, the more will be the opposing pressure.
At some stage there will be a perfect balance between the contraction(force) and expansion(force) helping the star to remain stable. The star thus remains stable for quiet a long period of time(million millions of years) till one of its forces gets weaker. Obviously, it can't be the gravitational force(contraction) that gets weaker.
The pressure inside the star eventually gets weaker, and the denser particles that gets cooled drift towards the center of the star, re surging the contraction process. This process continues till it reaches a stage where, the contraction force gets even by the repulsions between subatomic particles(electrons, protons, and neutrons). The star thus remains stable again for the second time.

The star that gets balanced by the repulsions between 'electrons' is termed as a
'White dwarf' with a radius of about few thousand miles and with a density of about hundreds of tons per cubic inch. And the one that is supported by the repulsions between protons and neutrons was popularly named as 'Neutron star' with a radius of about ten miles(only) and density, hundreds of millions of tons per cubic inch.

This would be the final stage of every known and unknown star that exist in our known and unknown universe, if the subatomic particles could move with out any limit. But, according to Einstein's Theory of relativity, nothing can travel faster than light.

Here comes the interesting question: What if the star is so heavy that it requires the electron(or proton or neutron) to move faster than light--to balance the immense contraction(force)?

These kinds of movements or repulsions among the subatomic particles are impossible according to the Theory of relativity and hence the star ends up in a gravitational collapse, and forms an infinitely dense region, popularly called as a 'Singularity'.
The star that gets vanished in to a 'singularity' still exerts the same, finite light trapping gravitational pull(can be more but not less) up to certain distance in space creating a 'Black hole' around it. The boundary of this 'Black hole', the 'Event horizon' is formed by the paths of light just managed to move around but can't escape.

Thus the whole Black hole formation was almost based on Einstein's 'Theory of relativity'.

What if the electrons under those special conditions(gravitational collapse) could move with out a speed limit--faster than light ?

There will be no 'Singularity', no 'Black hole' but will be a 'Black star' or 'Dark star' that still can trap light.
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The uncertainity principle by heisenberg

To get some clear understanding about the uncertainty principle, first, we need to know the quantum hypothesis.

Max Planck suggested that light, X-rays, and some other waves could not be emitted at the arbitrary rate, but in the form of energy packets called quanta.

According to the quantum hypothesis, each quantum--packet-- has certain amount of energy that was greater the higher the frequency of the waves. That implies that at higher frequencies, the emission of even a single quantum would require more energy than that was available. Thus the radiation at high frequencies gets reduced.

In order to predict the future position and velocity of a particle, one has to be able to determine its present position and velocity accurately. The only way to do this is to shine light on the particle and this will indicate its position. To determine more precisely one needs to use light of short wavelength(high frequency). Now, by Planck's quantum hypothesis, one cannot use an arbitrarily small amount of light; one has to use at least one quantum and this quantum will disturb the particle and change its velocity in a way that cannot be predicted. The more accurate one tries to measure the position, the greater will be the disturbance ( as it needs high energy quanta ). In other words, the more accurate one try to measure the position of a particle, the less accurate will be the speed and vice verse
This principle put an end to a notion(came from Newton's theory of gravity) that our universe is completely deterministic ( one can easily predict everything that would happen in the universe, if he knows its present state.)
It is only possible for the one who could observe the present state of universe with out disturbing it.

check this video.

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Ptolemy's geocentric Theory

Ptolemy proposed his Geocentric theory in the 2nd century A.D. What he did was just an elaboration of already existing idea that earth was in the center of universe, proposed by Aristotle, in to a complete cosmological model.

According to his theory, the earth stood at the center, surrounded by some eight spheres, the Moon, the Sun, the stars, and the five other planets known till the time: Mercury, Venus, Mars, Jupiter, and Saturn.

The first sphere supposedly carried Moon followed by Mercury, Venus, Sun, Mars, Jupiter, Saturn, and some fixed stars--eighth sphere--in the remaining seven spheres. The outer most sphere that is supposed to carry the so-called fixed stars, rotate across the sky; the stars thus remain fixed with respect to earth--according to him.

What about the region beyond the eighth sphere ?

He didn't explained that, as there is no way one can observe beyond stars--no telescope and no Galileo.

Does this theory provided a reasonably accurate system for predicting the positions of heavenly bodies in the sky ?

Yes, it was, but got one serious flaw: to predict the positions correctly, Ptolemy had to make an assumption that the moon followed a path that sometimes brought it twice as close to the earth as at other times. And that meant that the moon ought sometimes to appear twice as big as at other times!
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What makes a star shine ?

A star is formed when a large amount of gas (mostly hydrogen) starts to collapse in on itself due to its high gravitational attraction. As it contracts the atoms of the gas collide with each other more and more frequently and at greater and greater speeds--the gas heats up. Eventually, the gas will be so hot that when the hydrogen atoms collide they no longer bounce off each other, but instead coalesce to form helium. The heat thus released in this reaction, which is like a controlled hydrogen bomb explosion is what makes the star shine.
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