Black Holes

A black hole is a region of space with a gravitational field so strong that not even light can escape from it.

For example, when a star has burnt all of the available fuel in it’s core through nuclear fusion, it will start to collapse under its own weight. If the star is sufficiently massive, it is postulated that its gravitational field will become so intense that a black hole will form.

It has also been proposed, under the big bang model, that ‘primordial’ black holes may have been created by the extreme density of matter present soon after the creation of the universe.

Most, if not all, galaxies, including our own, are believed to contain ‘supermassive’ black holes at their centres. At the other end of the scale, ‘micro’ black holes are predicted to exist by some theories of quantum mechanics, and it might even become possible to create and study them in particle accelerators here on Earth.

The Event Horizon and Schwarzschild Radius

The closer an object is to a black hole (or any source of a gravitational field) the greater the escape velocity, i.e. the faster the object would needs to travel in order to escape. The distance from the centre of a (non-rotating) black hole within which any object would need to travel faster than light in order to escape is known as the Schwarzschild radius.  The more mass the black hole has, the larger its Schwarzschild radius. If it were possible to convert the mass of the Earth into a black hole, its Schwarzschild radius would be just 9 millimeters. However, the smallest black hole that can form from a collapsed star is likely to be around five to  ten times the mass of the Sun with a Schwarzschild radius of 15 to 30 kilometers.

Since nothing can travel faster than light, the Schwarzschild radius effectively marks the boundary of no return for any object falling into the black hole, and any events which occur within this distance from the centre cannot have any possible effect on an observer outside. Hence, the Schwarzschild radius is said to form the ‘event horizon’ of the black hole.

A rotating black hole behaves differently, however, and has an event horizon that is slightly smaller than its Schwarzschild radius.

The Schwarzschild radius is named after Karl Schwarzschild who, in 1916, first solved the Einstein’s field equations for a non-rotating, spherically-symmetric body.

The Singularity

According to the general theory of relativity, all the mass of a non-rotating black hole is compressed into a point of zero volume and infinite density at the very centre. This is known as a singularity.

Falling into a Black Hole

Your experience if you were to fall through the event horizon of a black hole would depend on the black hole’s mass.

A black hole around the mass of the Sun would have a Schwarzschild radius of around 3 kilometres and, at this distance, the tidal forces would be immense. This means that, if you were falling feet first, the gravitational pull on your feet would be much stronger than the gravitational pull on your head, stretching you out like spaghetti. In fact this “spaghettification” process (as it is often referred to) would have started at a much greater distance from the black hole and you would probably have been pulled apart long before you reached the event horizon.

For a supermassive black hole, of 10,000 solar masses, the Schwarzschild radius would be around 30,000 kilometers. At that distance the tidal forces would not be particularity strong, meaning that you would not be spaghettified as you passed the event horizon, although this would still occur at a closer distance to the centre. In fact, there would not be any obvious sign that you had passed the point of no return.

The Photon Sphere

Photons of light may orbit a simple non-rotating black hole at a distance of one and a half times the Schwarzschild radius. This is known as the photon sphere. Photons emitted by an object falling through the photon sphere could loop completely around the black hole, so it is possible that you could see the back of your own head.

For a rotating black hole, two possible circular photon orbits exists around the equatorial plane, one in the direction or rotation and one against it. The faster the black hole is spinning the greater the distance between these two orbits. Outside of the plane of the equator more complicated photon orbits are also possible.

Hawking Radiation

Quantum field theory predicts that the vacuum of space  in not empty. Due to the effect of the energy-time uncertainty principle, even a perfect vacuum is, in fact, teaming with “virtual particles“, which momentarily pop in and out of existence by “borrowing” energy from the vacuum.

These virtual particles are created in pairs – a particle and its antiparticle counterpart. If this pair of virtual particles is created on the very edge of a black hole’s event horizon, it is possible that one of the particles will fall into the black hole. The other particle, created just outside of the event horizon, can then take energy from the black hole to become a real particle and escape from the black hole. The constant stream of elementary particles (photons, electrons, quarks, gluons, etc.) created by this process near the event horizon is called Hawking radiation, after Steven Hawking who first proposed its existence in 1974.

Each particle radiated away via this process takes some of the energy, and hence the mass, of the black hole with it. Therefore a black hole will slowly reduce in size and possibly disappear altogether. However, a black hole the mass of the Sun would take around 2 × 1067 years to evaporate via this process, although a micro black hole would evaporate much quicker.

The radiation is as if it were emitted by a black body with a temperature that is inversely proportional to the black hole’s mass. A black hole with a mass roughly that of the moon or greater would, in fact, absorb more energy from the cosmic microwave background radiation than it emits through Hawking radiation. A micro black hole, however, would evaporate much more quickly and result in an explosion as the black hole  finally dissipates in a burst of Hawking radiation. This radiation from an evaporating black hole in space might even be detectable from Earth.

Some theories do not permit back holes to evaporate entirely, however, and suggest that the minimum size for a black hole would be around that of the Plank mass – the maximum size allowed for point-masses, which is around 22 micrograms or roughly the weight of a flea’s egg. A black hole this size would no longer be able to emit Hawking radiation, or absorb material via gravitation because of the quantised gaps between its allowed energy levels. Stable micro black holes of this nature could be the weakly interacting massive particles (WIMPs) that some theories propose make up dark matter.

Supermassive Black Holes

Calculations of the density of the nucleus at the centre of our galaxy, from the orbital speed of stars around it, suggest that it contains a black hole with the mass of around 4 million times that of the Sun.
It is postulated that all galaxies might contain these supermassive black holes at their centres.

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Astronomy, Cosmology, Astrophysics and Space Exploration

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