The Core

Calculating Hawking radiation

How bright are black holes?

The luminosity of a black body is given by the Stefan-Boltzmann formula:

: Stefan-Boltzmann constant;

A: Surface area of the black body
T: Temperature in Kelvin

1st: The relevant surface area for the Hawking radiation is the surface area of a sphere with the radius of the Schwarzschild radius, because that's where the radiation originates:

A sphere By Team C007571, ThinkQuest 2000.

We can substitute this in the formula for the luminosity:

2nd: We have already calculated the temperature of a black hole:

Putting this into the formula for the luminosity we get:

Some example calculations

A black hole the mass of the Earth

The luminosity of a black hole with the mass of the Earth equals:

Black hole in "The Hole Man"

The luminosity of the black hole in "The Hole Man":

35.7 gigawatts of hard gamma-radiation would certainly be absolutely deadly!

Black hole with the Luminosity of the sun

The Sun Courtesy of NASA. Nix NASA Image Eechange GRC Number: C-82-6709 Date Archived: 11/22/1982

How heavy will be a black hole with the luminosity of the sun?

A black hole of only 961kg of mass would have the same luminosity as the sun. And it would only be across! (diameter of the Schwarzschild radius). This black hole wouldn't be visible though, because it emits deadly gamma-radiation.

"Black holes aren't black - After Hawking they shine!"
Presented by Angie, Matthias and Thorsten
Team C007571,ThinkQuest Internet Challenge 2000.
Last modified: 2000-08-02.