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2024

Can light-rings self-gravitate?

Di Filippo, Francesco, Rezzolla, Luciano

Understand

In a spherically symmetric and static spacetime of a compact object, such as that of a Schwarzschild black hole, the light-ring is a 2-sphere where photons experience the only possible circular orbits.

As a "Gedankenexperiment", we imagine an advanced civilisation able to populate the light-ring of a nonrotating black hole of mass $M$ with photons having a fine-tuned impact parameter that allows their orbits to be exactly circular with radius $r=3M$.
As the number of photons in the light-ring increases in time, its mass will no longer be negligible and hence it will impact on the background spacetime, that is, it will "self-gravitate".
We here consider two different routes to assign a nonzero mass to the light-ring that are either based on a discrete concentration of photons on a specific radial location or on a suitable distribution of photons in a given region.