Introduction to Cosmology

Gravitational Waves 75

When gravitational waves travel through space-time they produce ripples of cur-
vature, an oscillatory stretching and squeezing of space-time analogous to the tidal
effect of the Moon on Earth. Any matter they pass through will feel this effect. Thus
a detector for gravitational waves is similar to a detector for the Moon’s tidal effect,
but the waves act on an exceedingly weaker scale.
Gravitational radiation travels with the speed of light and traverses matter unhin-
dered and unaltered. It may be that the carriers are particles,gravitons, with spin
퐽=2, but it is hard to understand how that could be verified. Perhaps, if a theory
were found combining gravitation and quantum mechanics, the particle nature of
gravitational radiation would be more meaningful.

Tensor Field. In contrast to the electromagnetic field, which is a vector field, the
gravitational field is a tensor field. The gravitational analogue of electromagnetic
dipole radiation cannot produce any effect because of the conservation of momentum:
any dipole radiation caused by the acceleration of an astronomical object is automat-
ically cancelled by an equal and opposite change in momentum in nearby objects.
Therefore, gravitational radiation is caused only by nonspherical symmetric accel-
erations of mass, which can be related to the quadrupole moment, and the oscilla-
tory stretch and squeeze produced is then described by two dimensionless wave fields
ℎ+andℎ×, which are associated with the gravitational wave’s two linear polarizations.
Ifℎ+describes the amplitude of polarization with respect to the푥-and푦-axes in the
horizontal plane,ℎ×describes the independent amplitude of polarization with respect
to the rotated axes푥+푦and푥−푦(see Figure 4.2). The relative tidal effect a detector
of length퐿may observe is then a linear combination of the two wave fields

훥퐿∕퐿=푎+ℎ+(푡)+푎×ℎ×(푡)≡ℎ(푡). (4.15)
The proper derivation of the quadrupole formula for the energy loss rate through
gravitational radiation of an oscillating body and the spatial strainℎ(푡)caused on
bodies elsewhere cannot be carried out here, it requires general relativity to be carried
out to high orders of covariant derivation. This complication is a benefit, however,
because it renders the detection of gravitational radiation an extremely sensitive test
of general relativity.

y y

z

x

+ polarization × polarization

x

z

Figure 4.2The lines of force associated with the two polarizations of a gravitational wave.
Reprinted with permission of A. Abramoviciet al.[3]. Copyright 1992 American Association
for the Advancement of Science.