ABSTRACT
This chapter discusses the geodesics of the Schwarzschild spacetime for massive and massless particles. It discusses the radial infall of a particle into a black hole, which will clarify the remarkable properties of the event horizon. Due to spherical symmetry, the Schwarzschild spacetime is invariant under rotations of the axes. The geodesic equations can be derived not only from the Equivalence Principle, but also from a variational principle. Massive particles move along timelike geodesics. In quantum field theory the existence of a negative energy particle implies that the vacuum state is unstable, because the creation of a cascade of particles with ever decreasing energy would be energetically favoured.
