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Formation of Black Holes

 

"Chandrasekhar realized, however, there is a limit to the repulsion that the exclusion principle can provide. The velocity of relativity limits the maximum difference in the velocities of matter particles in a star to the speed of light. This means that when the star got sufficiently dense, the repulsion caused by the exclusion principle would be less than the attraction of gravity. Chandrasekhar calculated that a cold star more than about one and a half times the mass of our sun would not be able to support itself against its own gravity. This limiting mass is now known as Chandrasekhar limit. If a star’s mass is less than the Chandrasekhar limit, it can eventually stop contracting and settle down to a possible final state as “White Dwarf”."

 

 

In addition to General Theory of Relativity & Quantum Mechanics, the twentieth century also celebrated another great partial theory of Nature, the Black Holes.

The term Black Hole is of very recent origin. It was coined in 1969 by American Scientist John Wheeler as a graphic description of an idea. A Cambridge don, John Michell, wrote a paper in 1783 in the Philosophical Transactions of the Royal Society of London in which he pointed out that a star that was sufficiently massive and compact would have such a strong gravitational field that even light could not escape. Any light that emitted from the surface of the star would be dragged back by the star's gravitational attraction before it could get very far. Michell suggested that there might be a large number of stars like this. Although we would not be able to see them because the light from them would not reach us, we would still feel their gravitational attraction. Such objects are what we call Black holes, because that is what they are : Black voids in space.

black-hole

A similar suggestion was made a few years later by the French Scientists the Marquis de Laplace, apparently independently of Michell. Interestingly enough, laplace included it in only the first and the second editions of his book The system of the world , and left it out of later editions; perhaps he decided that it was a crazy idea.

To understand how a black hole might be formed, we first need an understanding of the life cycle of a star. A star is formed when a large amount of gas (mostly Hydrogen) starts to collapse in on itself due to its gravitational attraction. As it contracts the atom of the gas collides with each other more and more frequently and at greater and greater speeds - 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 released in this reaction, which is like a controlled hydrogen bomb explosion, is what makes the star shine. This additional heat also increases the pressure of the gas until it is sufficient to balance the gravitational attraction, and the gas stops contracting. It is a bit like a balloon- there is a balance between- pressure of the air inside, which is trying to expand the balloon, and the tension in the rubber, which is trying to make the balloon smaller. Stars will remain stable like this for a long time, with heat from nuclear reactions balancing the gravitational attraction. Eventually the star will run out of hydrogen and other fuels. Paradoxically, the more a star starts off with, the sooner it runs off. This is because the more massive the star is, the hotter it needs to be to balance its gravitational attraction. And the hotter it is, the faster it will use up its fuel.

In 1928 an Indian graduate student, Subrahmanyan Chandrasekhar, set sail for England to study at Cambridge University. During his voyage from India, he worked out how big a star could be and still support itself against its own gravity after it had used up all its fuel. That wonderful idea was this :  When the star becomes small, the matter particles get very near to each other, and so according to the pauli exclusion principle, they must have very different velocities.  This makes them move away from each other and so tends to make the star expand. A star can therefore maintain itself at a constant radius by a balance between the attraction of gravity and the repulsion that arises from the exclusion principle, just as earlier in its life gravity was balanced by the heat.

Subrahmanyan-Chandrasekhar--Images

Chandrasekhar realized, however, there is a limit to the repulsion that the exclusion principle can provide. The velocity of relativity limits the maximum difference in the velocities of matter particles in a star to the speed of light. This means that when the star got sufficiently dense, the repulsion caused by the exclusion principle would be less than the attraction of gravity. Chandrasekhar calculated that a cold star more than about one and a half times the mass of our sun would not be able to support itself against its own gravity. This limiting mass is now known as Chandrasekhar limit. If a star’s mass is less than the Chandrasekhar limit, it can eventually stop contracting and settle down to a possible final state as “White Dwarf”.

 

 



Courtesy:1. “A Brief History of Time” by Stephen Hawking.

2. “A Briefer History of Time” by Stephen Hawking.

3. The Mathematical Theory of Black Holes by  Subrahmanyan Chandrasekhar

4. Various Documentaries

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Compiled by Dhiraj Sarmah.


  1. Harsh Rao

    20 November

    Heavy element production in case of galactic black holes- in the vicinity 'frame dragging' occurs- what happens in that case- some matter being dragged in would fuse, but in a drastically changed spacetime, wouldn't the energy equations change? could it be that elements of higher atomic wt than iron are produced, some of them spewed around and out by the black hole jets? would this be another source of higher elements?

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