Introduction

One of the key new phenomena that arises in general relativity is the existence of solutions to Einstein's equations which represent disturbances in the spacetime that propagate at the speed of light. Such solutions are called gravitational waves and this chapter will explore several features of them.

Propagating modes of gravity

Within the context of special relativity, it is easy to identify a wave solution. For example, a propagating, monochromatic spherical wave will be described by an amplitude that varies in space and time as f(t, r) ∞ r−1 exp[−iω(t − r)]. This disturbance clearly propagates from the origin with the speed of light (which is unity in our notation) with an amplitude that decreases as (1/r). Since the energy flux of a wave varies as the square of the amplitude, this wave transports a constant amount of energy across every spherical surface. Such a description can be easily made Lorentz covariant in terms of an appropriate wave vector, etc., and has an unambiguous meaning.

The situation is somewhat more complicated in the case of gravity for two (closely related) reasons. First, not all the components of the metric gab enjoy equal status in the dynamics of gravity. We saw in Section 6.3 that the g00 and g0α components do not propagate in general relativity. The equations governing them are constraint equations involving and and are analogous to the equation governing the gauge dependent mode in electrodynamics.