Gravitational Waves

Abstract

In the last chapter, we saw that in the weak-field approximation, Einstein’s equations for a perturbation of the Minkowski metric can be reduced to

$$ \square w_{ab} = - 16\pi T_{ab} ,$$

in the de Donder gauge [see (10.2)]. This is an inhomogeneous wave equation, with the energy-momentum tensor as source. It is strongly reminiscent of Maxwell’s equations for the four-potential in the Lorenz gauge and it has the same implication. Maxwell’s equations imply that moving charges generate electromagnetic waves. Einstein’s equations imply that moving masses generate gravitational waves.