Hawking Radiation

The Ninth Planet


Black holes are the dream of every space enthusiast and in recent years one name has cropped up very frequently in relation to black holes, Stephan Hawking. One of his revolutionary achievements was the idea that black holes aren’t completely black, i.e. they emit radiation. The prevailing classical theory of the time explained the formation of a black hole as a gravitational collapse which will settle down rapidly into an equilibrium state characterized by its mass, angular momentum and electric charge as characterized by the no hair theorem. These usually characterize a stationary solution of a black hole. However there is a classical phenomenon called super radiance in which electromagnetic waves incident in certain modes on a rotating or charged black holes are scattered with increased amplitude. This directly corresponds to an increase in the number of particles by stimulated emission.

The first law of black hole thermodynamics derived from the solutions of Einstein equations relates the change in mass of the black hole, the change in area, angular momentum, and the charge as follows,
First law

We notice that the right hand side, change in area is always non-negative, and thus arrive at the condition for negative change in mass, i.e. the energy from the black hole is lost to the wave packet which is scattered with the increased amplitude and is known as super radiance.

This classical concept, though works sufficiently well, breaks down when the mass of the black hole is reduced to be comparable to the Planck mass g. A quantum explanation is thus required to explain this phenomenon as an alternative to super radiance.

Hawking predicted that a black hole of M solar masses would glow like a blackbody of temperature kelvins. He explained this by the use of quantum fluctuations in vacuum as a result of energy-time uncertainty given as follows,
Formula
This allows virtual particles to exist for a brief duration as particle-antiparticle pairs. When this occurs near the event horizon, one of these particles may fall inside before they can annihilate each other while the other escapes as radiation. Since the particle emitted has positive energy the mass of the black hole must consequently decrease due to the increasing negative mass.

Hawking radiation has proved to be a gateway to explain various phenomena hitherto unexplained such as, the high amount of photons when compared to baryons and the theory of quantum gravity and has served to increase the understanding of the universe to the scientific community.