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Let's consider a Schwarzschild BH.

A photon (or a massive particle) crossing the event horizon cannot be static : the r (radial) coordinate becomes a temporal coordinate. Therefore, the photon falls towards the central singularity (r=0). There is no way for him to escape : the horizon is a static limit

Now, the photon sphere is the spherical region of space where the orbital speed is equal to c. Only photons can orbit on the photon sphere but these orbits are very unstable.

If a photon crosses this sphere, can it remain static (without moving or falling towards the central singularity) ? Is going towards the singularity the only movement it can describe ?

Now, let's consider a Kerr BH. There are two horizons (inner and outer). By definition, the ergosphere is the region of space between the static limit and the outer horizon. A photon in the ergosphere cannot be static (it has crossed the static limit) and falls towards the singularity.

But, what happens at the crossing of the outer horizon and, after, when crossing of the inner horizon ? What kind of trajectories are possible ?

Thanks,

Jeff

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# Schwarzschild & Kerr black holes geometries

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