1. Properties of Black Holes

A black hole is what remains when a large star dies. Any shining star exists because the pressure generated by the nuclear fusion reactor at its centre is high enough to counteract the gravity which is trying to collapse the star . When the star inevitably runs out of fuel, the gravity overcomes the nuclear pressure and the star collapses. This creates a much smaller object with a very high mass.

In order for any particle to leave the vicinity of any body of matter, it has to be travelling fast enough to overcome the gravity pulling it back to the centre of mass. The minimum speed that is required to leave a body of matter is called the escape velocity. French mathematician Pierre Laplace derived the following formula which tells us the escape velocity for any body of matter;
where V is escape velocity in metres per second, G is the universal gravity constant in N m² kg^-2, M is the mass of the body in kilograms and R is the radius of the body in metres. We can see by this formula that the escape velocity of a body is directly proportional to its mass and inversely proportional to its radius. For a planet such as the earth; , , V_esc = 11 202 m s^-1

Since light travels at 2.998 x10⁸ m s^-1, it can easily escape the earth’s atmosphere as this speed is much faster than the required 11 202 m s^-1, thus making the earth externally visible. A black hole, however, has a mass so high and a radius so small that the escape velocity exceeds the speed of light which is the fastest that anything can travel. Therefore, since neither light nor any signal can escape and any light travelling towards it is attracted along with any other particle that comes near, black holes are invisible. Light, instead, is trapped in an orbit by the intense gravitational force.

If a given mass is to become a black hole, it must become smaller than a mathematically determined radius called its Schwarzschild radius. The Schwarzschild radius is named after the German astronomer who derived the formula from Einstein’s theory of gravity. Since the escape velocity is found by the formula , if we substitute the escape velocity for the speed of light (c), we can find the Schwarzschild radius for the given mass by the new formula .

We can see by this formula that Schwarzschild radius is directly proportional to the body’s mass. For a mass of equal value to the earth; , , R_{Sch Earth} = 8.88 x10^-3 m or around 8.9mm.

The core and centre of a black hole is called the singularity. There is a spherical region around the singularity called the event horizon. This is the maximum height that any particle can possibly travel away from the centre of the black hole without falling back in. If any particle from outside reached this point, it cannot be retrieved from the black hole.

It is possible to predict the absolute temperature of a black hole solely from its mass by use of the formula;

Where T is the absolute temperature, k is Boltzmann constant, is Planck's constant over 2&pi, c is the speed of light, G is the universal gravity constant and M is the mass of the body.

Throughout the black hole’s existence, it radiates heat through complex processes defined by Quantum Electrodynamics and eventually evaporates. The discovery is attributed to Hawking and the energy a black hole dissipates is called Hawking Radiation. It is referred to as absolute temperature because it is measured on the Kelvin temperature scale. We can see by the formula that absolute temperature is inversely proportional to the body’s mass.


Because of the constant loss of energy due to Hawking Radiation, black holes have limited lives that can also be defined by a formula with the only variable being mass;
with K being a constant which encompasses other constants, namely;


Because black holes give off no light let alone any other kind of signal, it is quite difficult to detect them. They must be detected by the effect they have on the matter surrounding them as they cannot be observed directly. There are three main ways of detecting black holes. The first are estimates made due to the actions of bodies that are affected by the gravity of the black hole, either passing the black hole, orbiting or falling into the black hole. The second is a phenomenon known as the gravitational lens effect. Black holes can cause passing light to bend towards it. This may bring other celestial bodies into focus if observed from the ground. If there is no other explanation for the light to bend, it can be assumed that a black hole is causing the disturbance. The final common way of detecting black holes is the measurement of emitted radiation. When particles fall into black holes, they are heated to millions of degrees Kelvin and accelerated. These superheated particles emit X-rays which can be detected by X-ray telescopes.