Page 48 - A Brief History of Time - Stephen Hawking

A Brief History of Time - Stephen Hawking... Chapter 6
Europe, and Japan that will measure displacements of one part in a thousand million million million (1 with twenty-one
zeros after it), or less than the nucleus of an atom over a distance of ten miles.

Like light, gravitational waves carry energy away from the objects that emit them. One would therefore expect a system
of massive objects to settle down eventually to a stationary state, because the energy in any movement would be
carried away by the emission of gravitational waves. (It is rather like dropping a cork into water: at first it bobs up and
down a great deal, but as the ripples carry away its energy, it eventually settles down to a stationary state.) For
example, the movement of the earth in its orbit round the sun produces gravitational waves. The effect of the energy
loss will be to change the orbit of the earth so that gradually it gets nearer and nearer to the sun, eventually collides with
it, and settles down to a stationary state. The rate of energy loss in the case of the earth and the sun is very low – about
enough to run a small electric heater. This means it will take about a thousand million million million million years for the
earth to run into the sun, so there’s no immediate cause for worry! The change in the orbit of the earth is too slow to be
observed, but this same effect has been observed over the past few years occurring in the system called PSR 1913 +
16 (PSR stands for “pulsar,” a special type of neutron star that emits regular pulses of radio waves). This system
contains two neutron stars orbiting each other, and the energy they are losing by the emission of gravitational waves is
causing them to spiral in toward each other. This confirmation of general relativity won J. H. Taylor and R. A. Hulse the
Nobel Prize in 1993. It will take about three hundred million . years for them to collide. Just before they do, they will be
orbiting so fast that they will emit enough gravitational waves for detectors like LIGO to pick up.

During the gravitational collapse of a star to form a black hole, the movements would be much more rapid, so the rate at
which energy is carried away would be much higher. It would therefore not be too long ' before it settled down to a
stationary state. What would this final stage look like? One might suppose that it would depend on all the complex
features of the star from which it had formed – not only its mass and rate of rotation, but also the different densities of
various parts of the star, and the complicated movements of the gases within the star. And if black holes were as varied
as the objects that collapsed to form them, it might be very difficult to make any predictions about black holes in
general.

In 1967, however, the study of black holes was revolutionized by Werner Israel, a Canadian scientist (who was born in
Berlin, brought up in South Africa, and took his doctoral degree in Ireland). Israel showed that, according to general
relativity, non-rotating black holes must be very simple; they were perfectly spherical, their size depended only on their
mass, and any two such black holes with the same mass were identical. They could, in fact, be described by a
particular solution of Einstein’s equations that had been known since 1917, found by Karl Schwarzschild shortly after
the discovery of general relativity. At first many people, including Israel himself, argued that since black holes had to be
perfectly spherical, a black hole could only form from the collapse of a perfectly spherical object. Any real star – which
would never be perfectly spherical – could therefore only collapse to form a naked singularity.

There was, however, a different interpretation of Israel’s result, which was advocated by Roger Penrose and John
Wheeler in particular. They argued that the rapid movements involved in a star’s collapse would mean that the
gravitational waves it gave off would make it ever more spherical, and by the time it had settled down to a stationary
state, it would be precisely spherical. According to this view, any non-rotating star, however complicated its shape and
internal structure, would end up after gravitational collapse as a perfectly spherical black hole, whose size would
depend only on its mass. Further calculations supported this view, and it soon came to be adopted generally.
Israel’s result dealt with the case of black holes formed from non-rotating bodies only. In 1963, Roy Kerr, a New
Zealander, found a set of solutions of the equations of general relativity that described rotating black holes. These
“Kerr” black holes rotate at a constant rate, their size and shape depending only on their mass and rate of rotation. If the
rotation is zero, the black hole is perfectly round and the solution is identical to the Schwarzschild solution. If the
rotation is non-zero, the black hole bulges outward near its equator (just as the earth or the sun bulge due to their
rotation), and the faster it rotates, the more it bulges. So, to extend Israel’s result to include rotating bodies, it was
conjectured that any rotating body that collapsed to form a black hole would eventually settle down to a stationary state
described by the Kerr solution. In 1970 a colleague and fellow research student of mine at Cambridge, Brandon Carter,
took the first step toward proving this conjecture. He showed that, provided a stationary rotating black hole had an axis
of symmetry, like a spinning top, its size and shape would depend only on its mass and rate of rotation. Then, in 1971, I
proved that any stationary rotating black hole would indeed have such an axis of symmetry. Finally, in 1973, David
Robinson at Kings College, London, used Carter’s and my results to show that the conjecture had been correct: such a
black hole had indeed to be the Kerr solution. So after gravitational collapse a black hole must settle down into a state
in which it could be rotating, but not pulsating. Moreover, its size and shape would depend only on its mass and rate of
rotation, and not on the nature of the body that had collapsed to form it. This result became known by the maxim: “A
black hole has no hair.” The “no hair” theorem is of great practical importance, because it so greatly restricts the
possible types of black holes. One can therefore make detailed models of objects that might contain black holes and
compare the predictions of the models with observations. It also means that a very large amount of information about

file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/e.html (5 of 9) [2/20/2001 3:15:08 AM]