Both experimentally and theoretically, the curved spacetimes of general relativity are explored by studying how test particles and light rays move through them. This chapter derives and analyzes the equations governing the motion of test particles and light rays in a general curved spacetime. Only test particles free from any influences other than the curvature of spacetime (electric forces, for instance) are considered. Such particles are called free, or freely falling, in general relativity. In general relativity, free means free from any influences besides the curvature of spacetime. We begin with the equations of motion for test particles with nonvanishing rest mass moving on timelike world lines, and revisit the equations of motion for light rays.
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