Black
holes are peculiar objects with many strange properties, but most books and
articles have emphasised their exotic aspects, and obscured their fundamentally
simple nature. The description given below was first worked out by the French
mathematician Pierre Laplace in 1796, so they are not even a modern invention!
Before discussing black holes themselves we should think briefly about gravity.
What is Gravity?
Physicists recognize that the whole of the physical world can be described
in terms of four basic forces. Two of these are concerned with the innermost
structure of atoms, and a third, the electromagnetic force, dominates the
interaction of atoms with each other. The fourth, and by far the weakest
of these forces, is gravity. It is therefore only significant when enormous
numbers of atoms are collected together into objects the size of the Earth,
or bigger. Gravity is the dominant force in the lives and deaths of stars
and galaxies.
Any atom, or collection of atoms, has a property called mass, which measures
how much material there is in the object. On the surface of the Earth, the
gravity of the Earth pulls downwards on all masses giving the sensation of
weight. On the surface of the Moon this pull, or weight, is only one sixth
of that on the Earth, and so weight depends on where you are, whereas mass
is an intrinsic property of all objects.
In the 17th century Isaac Newton described gravity by saying that each
mass attracts every other mass in the universe with a force which depends
on how much material is present and how far away it is. In 1915 Albert Einstein
dramatically changed our idea of what gravity is, but Newton's description
is adequate for this article.
So, gravity is a universal attractive force which causes objects to `fall'
in the broadest sense, and tries to pull objects like stars and galaxies
together. It is bound to succeed unless it is opposed by some other force.
What is a Black Hole?
If a ball is thrown upwards from the surface of the Earth it reaches a
certain height and then falls back. The harder it is thrown, the higher it
goes. Laplace calculated the height it would reach for a given initial speed.
He found that the height increased faster than the speed, so that the height
became very large for a not very great speed. At a speed of 40,000 km/h (25000
mph, only 20 times faster than Concorde) the height becomes very great indeed
 it tends to infinity, as a mathematician would say. This speed is called
the `escape velocity' from the surface of the Earth, and is the speed which
must be achieved if a space craft is to reach the Moon or any of the planets.
Being a mathematician, Laplace solved the problem for all round bodies, not
just the Earth.
He found a very simple formula which tells us that the escape velocity, V, is given by,
v = (2GM/R)0.5
where G is a constant which defines how strong gravity is, M is the mass,
or amount of material, in the body and R is its radius. This formula says
that small but massive objects (i.e. small R and large M ), have large escape
velocities. For example if the Earth could be squeezed and made four times
smaller, the escape velocity would need to be twice as large. This surprisingly
simple derivation gives exactly the same answer as is obtained from the full
theory of relativity.
Light travels at just over 1000 million km/h (670 million mph), and in
1905 Albert Einstein proved that nothing can travel faster than light. The
above formula can be turned around to tell us what radius an object must
have if the escape velocity from its surface is to be the speed of light.
The answer is,
R=(2G/c2)M
where c is the speed of light. This particular radius, R, is called the
'Schwarzschild radius' in honour of the German astronomer who first derived
it from Einstein's theory of gravity. The formula tells us that the Schwarzschild
radius for the Earth is less than a centimetre, compared with its actual
radius of 6357 km. Values for some other astronomical objects are given in
the table below.
It might seem surprising that light can be thought of as behaving like
rocket ships and cricket balls! It was Einstein who showed that light can
be considered as a collection of particles, called photons, which have mass,
or more correctly energy, by virtue of the famous formula E=Mc^{2}
relating energy (E) and mass (M). Photons always travel at the same speed,
the speed of light, but when moving away from a gravitating object they lose
energy and, to an external observer, appear to be redder. It is this 'redshift'
which means that photons from a black hole ultimately lose all their energy
and become completely invisible.
If even light energy does not travel fast enough to escape (and nothing
can travel faster), then no signals of any kind can escape and the object
would be 'black'. The only indication of the presence of such an object is
the pull of its gravity. Away from the surface this is just the same as if
an ordinary object of the same mass were there. The presence of gravity means
that objects can fall into it, and hence 'hole'.
So, a black hole is an object which is so compact that the escape velocity from its surface is greater than the speed of
Object 
Mass (Solar Masses) 
Radius (km)

Escape Velocity (km/sec) 
Schwarzschild Radius 
Earth 
0.00000304 
6357 
11.3 
9.0mm 
Sun 
0.1 
696,000 
617 
2.95km 
White Dwarf 
0.8 
10,000 
5,000 
2.4km 
Neutron Star 
2 
8 
250,000 
5.9km 
Nucleus of Galaxy 
50,000,000 
? 
? 
147,500,000 km 
The speed of light is 299,800 km/sec (186,000 miles/sec). 11 km/sec is equivalent to 40,000 km/h (or 25,000 mph),
147,000,000 km is almost equal to the radius of the Earth's orbit round the Sun.
Where might we find Black Holes?
It is impossible to observe a black hole directly and so any black hole
candidates have to be identified by their effect on the matter surrounding
them. If no other explanation for the observed phenomena is valid then it
is likely that a black hole is present.
There are some objects that are good candidates for the presence of a black hole.
 Any star shines and survives because the pull of gravity, which is trying
to compress it, just balances the pressure generated by the nuclear furnace
at its centre, which is trying to expand it. Once the furnace runs out of
fuel, which must eventually happen, the pressure decreases, loses its battle
with gravity, and the star collapses. Astronomers believe that one of only
three things can happen to a star in this situation, depending on its mass.
A star less massive than the Sun collapses until it forms a `white dwarf',
with a radius of only a few thousand kilometers. If the star has between
one and four times the mass of the Sun, it can produce a `neutron star',
with a radius of just a few kilometers, and such a star might be recognised
as a `pulsar'. The relatively few stars with greater than four times the
mass of the Sun cannot avoid collapsing within their Schwarzschild radii
and becoming black holes. So, black holes may be the corpses of massive stars.
 Most astronomers believe that galaxies like the Milky Way were formed
from a large cloud of gas which collapsed and broke up into individual stars.
We now see the stars packed together most tightly in the centre, or nucleus.
It is possible that at the very centre there was too much matter to form
an ordinary star, or that the stars which did form were so close to each
other that they coalesced to form a black hole. It is therefore argued that
really massive black holes, equivalent to a hundred million stars like the
Sun, could exist at the centre of some galaxies.
How could we see a Black Hole?
Because black holes are small, and no signals escape from them, it might
seem an impossible task to find them. However, the force of gravity remains,
so if we detect gravity where there is no visible source of light then a
black hole may be responsible. This type of argument, by itself, is not very
convincing, and so we must look for other clues. If there is other material
around a black hole which might fall into it, then it will. There is then
a good chance that as it falls it will produce some detectable signal not
from the black hole itself, but from just outside it.
Most stars are not single, like the Sun, but are found in pairs, small
groups or large clusters. If a pair of stars have different masses then the
more massive one will burn up its nuclear fuel and may become a black hole,
whilst the other remains a normal star consuming its fuel more slowly. Gas
can then be sucked from the remaining star into the black hole. The gas becomes
very hot, with a temperature of millions of degrees, and will shine not with
visible light but with Xrays. These Xrays will have an observable effect
on the light output from the ordinary star. Since the star and black hole
go round each other every few days, we might expect to see regular variations
in the brightness and Xray output.
There are some Xray sources which have all the properties described above.
Unfortunately it is impossible to distinguish between a black hole and a
neutron star unless we can prove that the mass of the unseen component is
too great for a neutron star. Strong evidence was found by RGO astronomers
that one of these sources, called Cyg X1 (which means the first Xray source
discovered in the constellation of Cygnus), does indeed contain a black hole.
Things are rather different if there is a massive black hole in the centre
of a galaxy. It is possible there for a star to be swallowed by the black
hole. The pull of gravity on such a star will be so strong as to break it
up into its component atoms, and throw them out at high speed in all directions.
Some of the fragments will fall into the hole, increasing its mass, whilst
others could produce an outburst of radio waves, light and Xrays.
This is just the behaviour which is observed in galaxies of the type called
'Quasars' and may well be happening in a milder way in the centre of our
own Milky Way.
Astronomers from the RGO were part of a team who found that the galaxy
NGC 4151 contains about 1000 million times the mass of the Sun, concentrated
in a nuclear region whose diameter is no more than 4000 times the distance
between the Earth and the Sun. The most plausible explanation at present
is that most of this mass is in a black hole at the centre.