Black Hole Entropy

A black hole has an entropy proportional to its surface area, so it must have a temperature above absolute zero. What would be evidence for this temperature?

Answer

There should be radiation from the black hole that is, from the surrounding space, not from inside the black hole, because nothing can get out. This Hawking radiation was first calculated in the 1970s and awaits experimental verification.

By taking quantum mechanics into account, particles and antiparticles are being created continually via virtual pair creation in the vacuum. When this process occurs near a black hole, one particle of the pair may be “eaten” by the black hole and the other may escape. In the thermal equilibrium state, the amount of energy that the black hole loses to Hawking radiation is exactly balanced by the energy gained by swallowing other “thermal particles” that happen to be running around in the “thermal bath” in which the black hole finds itself.

The temperature of a nonrotating black hole is given by T = hc³/(8πkGM), where h is Planck’s constant and k is Boltzmann’s constant. Note that this expression connects gravitation, thermodynamics, and quantum mechanics. For black holes of a few solar masses, the temperature is only about 10^–6 K! The smaller black holes with little mass will be at a much higher temperature, contrary to intuition.