måndag 21 november 2022

Creating a black hole from non-linear optics

We know that

E = h f (1)

 and

E = m c ^2

Further, the Schwarzshild radius is

 

Schwarzshild radius

Assuming that the mass is uniformly spread out around the wavelength, or the size of one photon, we can look at the ratio between the wavelength and the Schwarzshild radius. Combining (1)-(3). When that quote becomes less than (approximately) 1, we have a higher mass density then what is required by a black hole:
Black hole criterion

Putting in the numbers, one arrives at
f_u = 5.2e24

This looks like the upper frequency a photon can have (Isn't also a bit scary that the exponent is 42...?).

If it was possible to create two photons with

and one can make them interact via some non-linear process, one can make a black hole from two photons.

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