What is the photon sphere around a black hole?

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.

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.