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The fact that light could theoretically create a black hole, which would be known as a kugelblitz, means that photons must curve spacetime. And since light can exist in an orbit (admittedly an unstable one) around a black hole, could two photons exist in an unstable orbit around each other?

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There is a class of solutions of general relativity called “geons”. These could be described as “clumps” of radiation (either electromagnetic or gravitational waves) held together by their own gravitational fields. Electromagnetic geon is not quite a kugelblitz, meaning that this amount of radiation has enough gravity to produce a photon sphere but the radiation does not collapse into the black hole because it has enough angular momentum. Such solutions are generally unstable, because eventually some radiation would escape, weakening the geon's gravity leading to more escaping radiation in a runaway instability, but lifetimes of such solutions could be much greater than typical light-crossing times based on their sizes.

But the above description of geon is applicable within purely classical Einstein–Maxwell theory. From the quantum viewpoint such electromagnetic geon would consist of a very large number of photons. If we try to decrease the number of photons needed to form a geon while keeping their gravity strong enough to form a photon sphere the typical energy of an individual photon must grow, so when the number of photons is small their energy would be comparable with the Planck energy. To answer whether just two of such energetic photons could orbit each other due to their gravitational interaction we would need the full theory of quantum gravity. Most likely, the notion of individual photons (separate from the admixture of gravitons and quanta of other fields) would not even make sense for such objects.

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What happens if two Planck energy photons with opposite momenta occupy one Planck volume? That should be a blackhole.

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