What is the photon sphere around a black hole?

• A. The radius where photons escape to infinity from any bound orbit.
• B. The region where matter can orbit at arbitrary speeds.
• C. The region where gravity is strong enough for photons to orbit the black hole, located at 1.5 Schwarzschild radii for a non-rotating BH.
• D. The surface of the event horizon.

Answer: (C)

Photon sphere is the region around a black hole where gravity is strong enough to bend light into a circular path. For a non-rotating (Schwarzschild) black hole, that circular photon orbit sits at r = 3GM/c^2, which is 1.5 times the Schwarzschild radius. So it lies just outside the event horizon (which is at 2GM/c^2). These orbits are unstable: a tiny perturbation will cause the photon to fall inward or escape. This concept specifically describes light paths, not matter orbits, and it’s not the surface of the event horizon.