The mystery of black holes

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 !

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'.

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.

Effects of a black hole

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).

Kerr's black hole

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. (Source : Sky and Telescope, J. Bergeron)