# Confining a photon to form a black hole

## Main Question or Discussion Point

How small a box can you confine a photon to before its mass is large enough to form a black hole?

I think you can make an estimate on the momentum (and therefore the energy) based on the size of the box using the Uncertainty Principle - knowing the energy gives you the mass via E=mc^2, but how do you figure out the mass and size needed to form the black hole?

Related Special and General Relativity News on Phys.org
That would be the Schwartzchild Radius, given by:

2Gm/c^2

Use E=hf and E=mc^2 to figure out the Schwartzchild radius for a photon of a given frequency.

Hi Bernarami,

The minimum frequency that a photon must have so that energy of the photon confined within its own wavelength has sufficient energy density to form a black hole is 1/(2Tp) where Tp is the Planck time interval. The wavelength of such a photon would be 2Lp where Lp is the Planck length and the mass equivalent of the photon energy would be Mp/2 where Mp is the Planck mass. Using the equation for the Schwarzschild radius of a black hole (R=2GM/c&2) the radius of the black hole photon would be GMp/c^2 = Lp and diameter would be the wavelength of the photon which would satisfy the conditions required for a stable standing wave.

Ref: http://en.wikipedia.org/wiki/Planck_units

Last edited: