# Confining a photon to form a black hole

1. May 12, 2008

### bernerami

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?

2. May 12, 2008

### peter0302

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.

3. May 12, 2008

### yuiop

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: May 12, 2008