Primordial Black Holes
Astronomy & Cosmology -
The Early Universe
(or "What Banged in the Big Bang?")
What Are They?
These are hypothetical objects that some suggest could have formed in the very early moments of the Big Bang. Generally, they would have been so small, minimum mass is the Planck mass, that quantum physics is required to describe them. Primordial black holes of very small mass would have evaporated by now due to Bekenstein/Hawking Radiation (see below). To have survived until today, a primordial black hole would need to have been of the order of one billion tons, but would still have had a Schwarzschild radius of only about 1.5 x 10-14 cm! The Schwarzschild radius of any object is proportional to its mass. Once an object is compressed within its Schwarzschild radius, it becomes a black hole. For an object that does not rotate, the surface at the Schwarzschild radius is its event horizon. As a comparison, to compress the Earth into a black hole, its Schwarzschild radius would be about one third of an inch (9mm)! To do the same for the sun, the radius would be less than two miles (3km).
In some proposed extra-dimensional theories, those involving large extra dimensions, it would be possible for the Large Hadron Collider (LHC) to produce microscopic black holes of approximately the Planck mass, with a corresponding Schwarzschild radius that would be close to the Planck length. These would evaporate almost instantaneously due to the affect of Bekenstein/Hawking Radiation (see below). Even if the black hole was stable, it would be of such small size compared to, say, a proton, and moving so fast, that it would leave the Earth before it could accrete any appreciable extra mass. Let us say the Schwarzschild radius of the black hole is around the Planck Length - 1.6 x 10-33 cm. The average spacing of atoms in a solid is between 2 x 10-12 cm and 3 x 10-12 cm. Thus, around 5 x 1020 of these microscopic black holes could fit between two atomic nuclei! The chances of a collision are slim indeed. Even if the black hole grew to, say, 50 billion tons, it would still be only the size of a proton! Remember; the total energy the LHC will reach is 14TeV. Cosmic rays reaching Earth from space can have energies in excess of 100 million times the LHC energy, and they have been hitting the Earth for billions of years.
Bekenstein/Hawking Radiation
Back in 1972, Jacob Bekenstein suggested that black holes should have a well-defined entropy related to their surface area, and a non-zero temperature. Stephen Hawking opposed this idea quite vociferously! Soon after, however, Hawking realized that there was a way for a black hole to loose mass through quantum mechanical effects, also known as "Black Hole Evaporation". There is a very simple non-mathematical way to consider this process. Quantum mechanics predicts that vacuum fluctuations cause virtual particle-antiparticle pairs to appear in copious quantities every where. Normally, these almost immediately annihilate with each other, very quickly returning the energy that was borrowed as required by quantum mechanics. Consider, for example, an electron/positron pair produced near the event horizon of a black hole. Before the pair has a chance to annihilate, one of the particles is drawn into the black hole. The other particle becomes a "real" particle and goes on its merry way. As "there is no such thing as a free lunch", the energy to create the particle must be paid back, and it comes from the black hole. As energy is equivalent to mass, E = mc2, this results in a tiny decrease in the mass of the black hole. From the outside, it appears that the particle has been emitted by the black hole which is the Bekenstein/Hawking Radiation. Any black hole of mass more than about that of the Moon absorbs at least as much energy from the cosmic background as it does from the Bekenstein/Hawking effect, so it is only very small primordial black holes that would loose mass overall and evaporate.
If a black hole absorbs no energy, than a one solar mass black hole would evaporate in about 2.0 × 1067 years. The universe is only about 13.7 × 109 years old! A black hole of only about 1011 kg (about one hundred million tons), however, would evaporate in about 2 2/3 billion years, so it is possible that some primordial black holes are evaporating around us today.