ABSTRACT
This chapter discusses the gravitational waves emitted by dynamical systems described by a stress-energy tensor, on the assumption that the gravitational field is weak and that the speed of the bodies is small compared to the speed of light. This assumption is called the quadrupole approximation since in this regime the emitted radiation depends only on the quadrupole moment of the source. The quadrupole approximation allows to estimate the gravitational energy and the waveforms emitted by these systems. The chapter uses Latin indices for the space components of tensors, and Greek indices for the spacetime components. General Relativity predicts that gravitational waves do not include monopolar and dipolar contributions.
