An Etymological Dictionary of Astronomy and Astrophysics

The temperature inferred for a → black hole based on the → Hawking radiation.

For a → Schwarzschild black hole, one has

T_H = ħc³/(8πGMk) where ħ is the → reduced Planck’s constant, c is the → speed of light, G is the → gravitational constant, M is the mass, and
k is → Boltzmann’s constant. The formula can approximately be written as: T_H≅ 6.2 x 10^-8 (Msun/M) K. Thus radiation from a solar mass black hole would be exceedingly cold, about 5 x 10⁷ times colder than the → cosmic microwave background. Larger black holes would be colder still. Moreover, smaller black holes would have higher temperatures. A → mini black hole of mass about 10¹⁵ g would have T_H≅ 10¹¹ K.

Etymology (EN): → Hawking radiation; → temperature.