Apparently a photon sphere is a region of space where gravity is strong enough to cause light to travel in orbits. The radius of the photon sphere is given by(adsbygoogle = window.adsbygoogle || []).push({});

[tex] r = \frac{3 G M}{c^2}[/tex]

If one had a photon that was energetic enough then its own gravity would trap it in its own photon sphere. I believe this is John Wheeler's geon idea.

Imagine that a photon is forced into a closed orbit. By analogy with the Bohr atom its orbital angular momentum should be quantized such that:

[tex] p \ r = n \hbar [/tex]

Using the relation between energy and momentum for photons, [itex] E = p \ c [/itex], we find

[tex] E = \frac{n \hbar c}{r} [/tex]

Using the Einstein relation, [itex]E = M c^2[/itex], we can substitute the quantized photon mass/energy into the photon sphere equation. By eliminating [itex]r[/itex] we find that the mass of the resulting object is given by:

[tex] M = \sqrt{\frac{n}{3}} \sqrt{\frac{\hbar c}{G}}[/tex]

[tex] M = \sqrt{\frac{n}{3}} M_{planck} [/tex]

I know that John Wheeler concluded that classical geons are not stable. Classical photon orbits are not stable.

But could a quantum geon produced by a coherent photon orbit as described above be stable in the same way that a Bohr atom is stable?

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# Quantum geons?

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