In 1916, the German astronomer Schwarzschild, with the support
of Einstein's works, calculated the size of a star whose escape
velocity would be equal to the speed of light .

This speed is an absolute limit, and according to relativity, nothing can go
faster.

What's more, we know that the size of a neutron star decreases
when its mass increases, because gravity becomes stronger than the degeneracy
pressure.

If the mass of such a star increases, there comes a time, called the Oppenheimer-Volkoff
limit, when the escape velocity
becomes equal to the speed of light, and nothing will be able to escape the
star.

Let us notice that the cohesion of a neutron star is also depending of the strong nuclear interaction. As the behaviour of this interaction is poorly understood under a high gravity, the Oppenheimer-Volkoff limit is not precisely known. It is contained between 1.5 and 3 solar masses.

On this graph, you can see that the size of a black hole horizon
(the Schwarzschild radius)
is equal to a neutron star size when its mass is about 2.5 Solar masses
(this mass is called the Oppenheimer-Volkoff limit).

Notice that, for a white dwarf or a neutron star, the size decreases when the mass increases !

Notice that, for a white dwarf or a neutron star, the size decreases when the mass increases !

If nothing, not even light, can't escape, this star becomes invisible
: Such an object is called a black hole.

The black hole has no material surface ; the original matter of the star is
shrunk to an infinitely dense point, called a singularity.

The "surface" of the black hole is called the horizon, its size is
called 'Schwarzschild radius'.

If G is the gravitational constant and M the mass of a
body whose radius is R, the escape velocity is .

In the case of a black hole, this velocity is equal to c the speed of light,

hence the Schwarzschild radius of a black hole is expressed as

In the case of a black hole, this velocity is equal to c the speed of light,

hence the Schwarzschild radius of a black hole is expressed as

Everything which could happen beyond the horizon is trapped, and can only increase the mass of the black hole.

Contraty to Hollywood movies, a black hole is not a "cosmic vacuum cleaner" : it can only catch objects which come very near. If we replaced the Sun with a black hole, we couldn't notice the difference (at least in terms of gravity, we would miss the heat !)

We can view two scenarios to explain the creation of a black hole :

- a neutron star is part of a binary system, and its mass increases by the pulling of the matter of the other star - accretion disk phenomenon, like a nova.
- the collapse of a hypernova leads to the direct formation of a black hole.

It must be said that some people, with supporting arguments,
think that a black hole is physically impossible. All the theory about black holes must be considered with the utmost care, by keeping in mind the fact that it's only a mathematical theory, at the moment, but whose physical reality is becoming more and more obvious. |

Einstein's general relativity describes gravity as a curvature
of the space-time continuum. The more concentrated the mass, the more curvature
you obtain.

If we draw the framework of space-time as a plane (actually there are 4 dimensions
: 3 for the space, and one for time), we can visualize this curvature, in an
illustrative way.

In the case of a black hole, the curvature may have no end : there would be a tear in the fabric of space-time . We must use the conditional here, because we are entering a field where there is no absolute certainty...

In this space-time, light travels along
the shortest path. If space is flat, i.e. non-curved, the path is of course
a straight line.

Near a mass, this is no longer true : the mass can act towards the light like
an optical lens.

The effect of a gravitational lens appears here. |

**Warning : this picture is very simplistic. It is the whole
of space-time which is curved. This means that, not only space, but time itself
is modified by the central mass.**

The more concentrated the mass, the larger the effect. This is a way to detect a black hole if it lies between a star and us.

By analysing the same effect of the bending of light rays, we can try to guess the appearance of a black hole with an accretion disk.

Because of the bending of light, a black hole would
appear like this hat shape.

(source J-A. Marck/J-P. Luminet).

The idea of the black hole is the result of calculations from
general relativity, due to Schwarzschild. He calculated the size of the horizon
of a static black hole. Kerr improved the calculations when the black hole is
rotating.

In this case, the curvature of space-time looks different, and the singularity
is no longer concentrated into a point, but into a ring inside the horizon.

In this case, space-time is not only curved like a funnel, but it's twisted
to follow the rotation of the black hole.

A light ray, directed at the black hole, would follow the red path.

A light ray, directed at the black hole, would follow the red path.

(Source : Sky and Telescope, J. Bergeron)

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