Page 45 - A Brief History of Time - Stephen Hawking

A Brief History of Time - Stephen Hawking... Chapter 6
gravity was balanced by the heat.

Chandrasekhar realized, however, that there is a limit to the repulsion that the exclusion principle can provide. The
theory of relativity limits the maximum difference in the velocities of the matter particles in the 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 of more than about one and a half times the mass of
the sun would not be able to support itself against its own gravity. (This mass is now known as the Chandrasekhar
limit.) A similar discovery was made about the same time by the Russian scientist Lev Davidovich Landau.

This had serious implications for the ultimate fate of massive stars. 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 a “white dwarf” with a radius of a few
thousand miles and a density of hundreds of tons per cubic inch. A white dwarf is supported by the exclusion principle
repulsion between the electrons in its matter. We observe a large number of these white dwarf stars. One of the first to
be discovered is a star that is orbiting around Sirius, the brightest star in the night sky.
Landau pointed out that there was another possible final state for a star, also with a limiting mass of about one or two
times the mass of the sun but much smaller even than a white dwarf. These stars would be supported by the exclusion
principle repulsion between neutrons and protons, rather than between electrons. They were therefore called neutron
stars. They would have a radius of only ten miles or so and a density of hundreds of millions of tons per cubic inch. At
the time they were first predicted, there was no way that neutron stars could be observed. They were not actually
detected until much later.

Stars with masses above the Chandrasekhar limit, on the other hand, have a big problem when they come to the end of
their fuel. In some cases they may explode or manage to throw off enough matter to reduce their mass below the limit
and so avoid catastrophic gravitational collapse, but it was difficult to believe that this always happened, no matter how
big the star. How would it know that it had to lose weight? And even if every star managed to lose enough mass to
avoid collapse, what would happen if you added more mass to a white dwarf 'or neutron star to take it over the limit?
Would it collapse to infinite density? Eddington was shocked by that implication, and he refused to believe
Chandrasekhar’s result. Eddington thought it was simply not possible that a star could collapse to a point. This was the
view of most scientists: Einstein himself wrote a paper in which he claimed that stars would not shrink to zero size. The
hostility of other scientists, particularly Eddington, his former teacher and the leading authority on the structure of stars,
persuaded Chandrasekhar to abandon this line of work and turn instead to other problems in astronomy, such as the
motion of star clusters. However, when he was awarded the Nobel Prize in 1983, it was, at least in part, for his early
work on the limiting mass of cold stars.

Chandrasekhar had shown that the exclusion principle could not halt the collapse of a star more massive than the
Chandrasekhar limit, but the problem of understanding what would happen to such a star, according to general
relativity, was first solved by a young American, Robert Oppenheimer, in 1939. His result, however, suggested that
there would be no observational consequences that could be detected by the telescopes of the day. Then World War II
intervened and Oppenheimer himself became closely involved in the atom bomb project. After the war the problem of
gravitational collapse was largely forgotten as most scientists became caught up in what happens on the scale of the
atom and its nucleus. In the 1960s, however, interest in the large-scale problems of astronomy and cosmology was
revived by a great increase in the number and range of astronomical observations brought about by the application of
modern technology. Oppenheimer’s work was then rediscovered and extended by a number of people.

The picture that we now have from Oppenheimer’s work is as follows. The gravitational field of the star changes the
paths of light rays in space-time from what they would have been had the star not been present. The light cones, which
indicate the paths followed in space and time by flashes of light emitted from their tips, are bent slightly inward near the
surface of the star. This can be seen in the bending of light from distant stars observed during an eclipse of the sun. As
the star contracts, the gravitational field at its surface gets stronger and the light cones get bent inward more. This
makes it more difficult for light from the star to escape, and the light appears dimmer and redder to an observer at a
distance. Eventually, when the star has shrunk to a certain critical radius, the gravitational field at the surface becomes
so strong that the light cones are bent inward so much that light can no longer escape Figure 6:1.

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