Black Hole Thermodynamics

One of the strangest and most beautiful discoveries in physics is that black holes obey laws that look almost exactly like the laws of thermodynamics, the science of heat, energy and disorder. This correspondence, black hole thermodynamics, sits at the very centre of Hawking's legacy.

The four laws

In a celebrated 1973 paper, James Bardeen, Brandon Carter and Stephen Hawking set out four laws of black hole mechanics that parallel the four laws of thermodynamics. The zeroth law says the gravity at the surface of a settled black hole is uniform all over its event horizon, just as temperature is uniform throughout a system in equilibrium. The first law relates changes in a black hole's mass to changes in its area, spin and charge, mirroring the conservation of energy. The second law is Hawking's area theorem: the total horizon area never decreases, exactly as entropy never decreases. The third law says you cannot reduce the surface gravity to zero in any finite process.

From analogy to reality

At first, the resemblance looked like a tantalising coincidence. If a black hole truly had a temperature, it would have to radiate, and a black hole was supposed to emit nothing. Hawking himself was sceptical that the parallel was anything more than mathematical.

Then came his great discovery. By applying quantum mechanics near the horizon, Hawking showed that black holes do radiate, with a real temperature proportional to their surface gravity. This is Hawking radiation. In one stroke it transformed the analogy into literal physics: a black hole's surface gravity really is its temperature, and its horizon area really is a measure of its entropy, the Bekenstein-Hawking entropy. The laws of black hole mechanics are the laws of thermodynamics, applied to the most extreme objects in the universe, and the deep meaning of that fact is still being unravelled.