# ## Intuitive

Explanations in this section should contain no formulas, but instead colloquial things like you would hear them during a coffee break or at a cocktail party.

## Concrete

$$T= \frac{\hbar c^3}{8 \pi G M k_B} ,$$

where $k_B$ is the Boltzmann constant, $c$ the speed of light, $G$ the gravitational constant, $\hbar$ the reduced Planck constant and $M$ the mass of the black hole.

The temperature of a black hole is tiny. Putting in the numbers yields

$$T= 6.169 \cdot 10^{-8} \text{ K } \ \frac{M_\odot }{M},$$ where $M_\odot$ is the mass of the sun. In words this means that black hole with a mass equal to the mass of our sun would have a temperature of only $10^{-8}$ K. If the black hole is heavier, the temperature gets even tinier.

## Abstract

The motto in this section is: the higher the level of abstraction, the better.

## Why is it interesting?

This formula for the Hawking radiation shows why black holes are so important and interesting. In this little formula everything comes together:

• Quantum mechanics, in the form of $\hbar$
• Gravity, in the form of $G$

It tells us that black holes are laboratories for quantum gravity. 