If you were standing on a railway track that circled a non rotating black hole and that railway track was located at the photon sphere, the track would appear straight, not curved.
Orbiting Light
Is it possible for light to go into orbit around a celestial body?
Providing that body is a black hole and that the light is at a distance of 1.5 times the distance of the Schwarzschild radius (i.e. at the photon sphere), yes it can. But light in this orbit is highly unstable. Unlike a satellite orbiting a planet, where the satellite's velocity is able to adjust (speed up and slow down in accordance with Newton's laws) to match any slight eccentricity in its orbit, photons can only travel at a specific speed, c. Light can only orbit a black hole, therefore, if it is traveling in a perfect circle with the black hole at its exact centre. Any slight deviation from this and the light would head away from or spiral into the black hole.
So if you were able to somehow able to suspend yourself at this distance and then shine a laser beam exactly perpendicular to the line connecting you and the black hole, the beam would appear to be travel in a straight line but would in fact travel in a circle. Under this scenario you would be able to see the back of your head. You and your image woiuld occupy the same space coordinates but at different times.
Is it possible for light to go into orbit around a celestial body?
Providing that body is a black hole and that the light is at a distance of 1.5 times the distance of the Schwarzschild radius (i.e. at the photon sphere), yes it can. But light in this orbit is highly unstable. Unlike a satellite orbiting a planet, where the satellite's velocity is able to adjust (speed up and slow down in accordance with Newton's laws) to match any slight eccentricity in its orbit, photons can only travel at a specific speed, c. Light can only orbit a black hole, therefore, if it is traveling in a perfect circle with the black hole at its exact centre. Any slight deviation from this and the light would head away from or spiral into the black hole.
So if you were able to somehow able to suspend yourself at this distance and then shine a laser beam exactly perpendicular to the line connecting you and the black hole, the beam would appear to be travel in a straight line but would in fact travel in a circle. Under this scenario you would be able to see the back of your head. You and your image woiuld occupy the same space coordinates but at different times.
