# If i had a black hole of 20 solar masses, how much energy would it radiate?

1. Dec 21, 2007

### rubecuber

If i had a black hole of 20 solar masses, how much energy would it radiate?

2. Dec 21, 2007

### mathman

If you are referring to Hawking radiation, essentially none. Black holes are "observed" by their effect on accreting matter, which is very energetic.

3. Dec 22, 2007

### George Jones

Staff Emeritus
Let's assume your 20 solar-mass black hole is totally isolated, i.e., nothing is falling in.

The temperature (Kelvin) of the black hole is given by

$$T = \frac{\hbar c^3}{8 \pi k G M}.$$

Using the stuff below, can you work out the temperature of the black hole?

$$c=3.00\times10^8m/s[/itex] [tex]G=6.67\times 10^{-11} m^3 kg^{-1} s^{-2}$$
$$\hbar=1.054\times 10^{-34} J.s$$
$$k=1.381\times 10^{-23} J/K$$
$$M_{Sun}=1.989\times10^{30} kg$$

4. Dec 22, 2007

### marcus

mathman and George Jones already answered. the smaller and less massive holes are hotter and radiate more watts

big massive ones (like solar mass and up) are colder than the 2.75 kelvin microwave background----they'd be net absorbers under most circumstances

you could turn the question around and ask how small would a BH have to be for it to have an interesting temperature, and radiate heat at some noticeable rate. you know, could you heat a cup of coffee with one? I don't know the answer but George Jones has provided the necessary equations I think.