Particles and Light Motion in Schwarzschild Spacetime

Abstract

This Chapter studies particle and light motion near the Schwarzschild black hole. We focus mainly on those aspects of the motion that are specific for the black holes and that are of the most interest for astrophysical applications. For the particle motion, we discuss types of the orbits, gravitational capture, circular orbits near the black hole, the innermost stable orbits, the relativistic version of the Kepler’ laws. For the light propagation, we describe light trajectories, critical impact parameter for light capture by a black hole, bending angle and time delay for light scattering, including their asymptotic behavior in the near critical regime (Darwin’s formulas). A method of ray tracing in the Schwarzschild spacetime is used for calculation of different observable effects, such as frequency shift of light emitted by particles moving around a black hole, and lensing properties of black holes. We also briefly discuss weakly magnetized black holes and charged particle motion in their vicinity. At the end of the Chapter particle and light motion is analyzed in the higher dimensional spherical black holes.