Question

What is Hawking radiation and its relationship to the Stefan's Law?

Answer 1

Hawking radiation is black body radiation predicted to be emitted by black holes due to quantum effects near the event horizon. It is named after the cosmologist Stephen Hawking.

Stefan's law is a law that describes the power radiated by a black hole in terms of its temperature. Specifically, the Stefan–Boltzmann law states that the total energy radiated per unit surface area of a black body across all wavelengths per unit time (also known as the black-body radiant exitance or emissive power), `j^{\star}`, is directly proportional to the fourth power of the black body's thermodynamic temperature T:

The constant of proportionality σ, called the Stefan–Boltzmann constant or Stefan's constant, derives from other known constants of nature. The value of the constant is

The two are related in so far that Hawking radiation is emitted from a black hole due to the quantum effects near the event horizon, and Stefan's law is met in the thermodynamics of black holes in the form of Hawking radiation.

Sources: http://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law

http://en.wikipedia.org/wiki/Hawking_radiation