Summary

A light flash moves along a null geodesic, a locally straight worldline with zero proper time between any two events on this worldline (Figure 1). The same is true near a black hole. Every shell observer and every local free-float observer measures the speed of light to have the standard value unity. In contrast, the records of the Schwarzschild bookkeeper show light to move at a calculated speed less than unity near a black hole, with different radial and tangential speeds.

Near the horizon, the value of both components goes to zero. The reduced speed of light has been verified by Shapiro and his colleagues for radio waves passing close to Sun. (See Project E, Light Slowed Near Sun.)

A single constant of the motion, the impact parameter b, characterizes the trajectory of light around a center of gravitational attraction. For light that starts from a great distance, the value of this impact parameter is the perpendicular distance between the initial path of the light and the parallel path of a test particle that plunges radially straight into the black hole (Figure 2, page 5-6). For light that starts nearer to the black hole, the value of b must be derived from the tangential component of light velocity as measured by a local shell observer (Sample Problem 1, page 5-10).

A qualitative description of the motion of light derives easily from a plot of the constant quantity 1/b2 on the same graph as the effective potential for the motion of light (Figure 5, page 5-13).

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