ABSTRACT
This chapter discusses the geodesic motion of massive and massless particles in Kerr’s spacetime. It discusses the motion outside the outer horizon, because this is the region relevant for astrophysical observations. The chapter discusses a set of four algebraic equations for the components of the particle four-velocity, i.e. of the tangent vector to the geodesic. Since the Kerr spacetime is axisymmetric the orbits are generically non-planar; the only orbits which are planar are those along the rotational axis with initial velocity parallel to it, and those which start in the equatorial plane. The chapter derives the geodesic equations in the general case using the Hamilton-Jacobi approach, and shows how the Carter constant emerges in this framework. It discusses the geodesic motion of a particle on the equatorial plane of the Kerr metric in Boyer-Lindquist coordinates.
