In Schwarzschild spacetime, the photon sphere is located at what radius relative to the Schwarzschild radius?

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Multiple Choice

In Schwarzschild spacetime, the photon sphere is located at what radius relative to the Schwarzschild radius?

Explanation:
In Schwarzschild spacetime, there exists a special radius where light can orbit the black hole in a circular path. For a non-rotating black hole, this photon-sphere radius is r = 3GM/c^2. Since the Schwarzschild radius is RS = 2GM/c^2, the photon sphere sits at 1.5 times the Schwarzschild radius (r = 3GM/c^2 = 1.5 RS). It lies outside the event horizon, but quite close to it. These orbits are unstable: a tiny perturbation will cause the photon to either spiral into the black hole or escape to infinity, so the orbit is not stable over time.

In Schwarzschild spacetime, there exists a special radius where light can orbit the black hole in a circular path. For a non-rotating black hole, this photon-sphere radius is r = 3GM/c^2. Since the Schwarzschild radius is RS = 2GM/c^2, the photon sphere sits at 1.5 times the Schwarzschild radius (r = 3GM/c^2 = 1.5 RS). It lies outside the event horizon, but quite close to it. These orbits are unstable: a tiny perturbation will cause the photon to either spiral into the black hole or escape to infinity, so the orbit is not stable over time.

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