Number of words: 790

A black hole is then an object on whose surface the force of gravity is such that even light will not escape from it. But this statement assumes that light is affected by gravity. That light is affected by gravity is a prediction of the general theory of relativity. Indeed, one of the predictions of the general theory was that if a light ray grazes the surface of the sun, it would be deflected by 1.75 seconds of arc. This is a very small effect. Nevertheless, the measurements by the British expeditions led by Eddington and Dawson in the early months of 1919 verified this. So we know that a light ray grazing the surface of the sun will be deflected by 1.75 seconds of an arc. Now, the sun has a radius of about 700,000 km and its mass is about 2x 10″ gm. Suppose the sun was compressed by a factor 100, so that its radius is not 700,000 km but 7000 km. Then light will be deflected by 100 times the value. 100 times 1.75 seconds is close to three minutes. The smaller the fraction of the radius to which you squeeze the sun, the larger will be the deflection of light. It can be shown that if the sun could be compressed to a radius of 3.75 km then light will go round and round the sun like a satellite, instead of travelling in a straight line. If the mass of the sun is further compressed to a radius of 2.5 km, the force of gravity on it will be so large that even light will nor escape from it. Then it cannot be self-luminescent; you can’t see it and that is why you call it a black hole!

But, at this point you may say: If the sun with its present radius of 700,000 km and a mean density of 1.5 gm/cc (the density of water is 1 gm/cc) were compressed to a radius of only 2.5 km, its density would increase to something like 10″ gm/cc (i.e. 100 million million gm/cc)!

One’s natural instinct would be to ask: Isn’t that so high a density that it is impossible? It is not! Those densities are entirely within the realm of reality. For example, if you take an atom of gold or an atom of copper and you look at the nucleus, the entire mass of the nucleus is confined to a radius which is 10^-13 cm and if you ask what the nuclear density is you will find that the density is of the same order as that of the compressed sun. So in reality there exist objects on the earth, viz., the nuclei of atoms, which have these densities. So to contemplate a density of 10¹³ or 10¹⁵ gm/cc is not in itself absurd. On the other hand, if you take an ordinary gas and say that you want to reach a density of 10¹³ or 10¹⁵ gm/cc, you must compress it in such a way that all the nuclei of the atoms are packed one on top of the other. To do this you have to get rid of all the electrons and bring the nuclei close together; but these nuclei have all the same type (positive) of charge and hence they repel each other; so you have to press them so close that you overcome the core-energy and in practice you may not be able to do that.

This is why normal matter does not have such high density. But during the natural course of evolution of stars it is possible for matter in a star to condense or collapse to such small dimensions that these densities are obtained. This conclusion is based on very, very simple arguments, both observational and theoretical. You may ask: why should a star like the sun which has a mean density of only 1.5 gm/cc during its evolution reach such high densities as 103 gm/cc? The answer is that it is a structure which is supported by pressure. Where does the pressure come from! The pressure comes from the fact that radiation is flowing through it, and if a stage should come when radiation no longer flows through it, you would have a situation that the pressure cannot support the structure. It is like removing the foundation of a building; then it will collapse. So the nature of argument, which is very simple, is that if a time should come when the sun has exhausted its energy, the flow of radiation would cease and then it would collapse. At this point you may ask: will this happen? The answer is yes.

Excerpted from page 41-43  of  S. Chandrasekhar ‘Man of Science ’ by A.P.J. Abdul Kalam