2.1 Gravitational field vs gravitational waves
Gravitational waves are propagating oscillations of the gravitational field, just as light and radio
waves are propagating oscillations of the electromagnetic field. Whereas light and radio waves
are emitted by accelerated electrically-charged particles, gravitational waves are emitted by
accelerated masses. However, since there is only one sign of mass, gravitational waves never
exist on their own: they are never more than a small part of the overall external gravitational
field of the emitter. One may wonder, therefore, how it is possible to infer the presence of an
astronomical body by the gravitational waves that it emits, when it is clearly not possible to sense its
much larger stationary (essentially Newtonian) gravitational potential. There are, in fact, two
reasons:
- In general relativity, the effects of both the stationary field and gravitational radiation are
described by the tidal forces they produce on free test masses. In other words, single geodesics
alone cannot detect gravity or gravitational radiation; we need at least a pair of geodesics. While
the stationary tidal force due to the Newtonian potential
of a self-gravitating source at a
distance
falls off as
, the tidal force due to the gravitational wave amplitude
that it emits at wavelength
decreases as
. Therefore, the stationary
coulomb gravitational potential is the dominant tidal force close to the gravitating body (in
the near zone, where
). However, in the far zone (
) the tidal effect of the waves
is much stronger.
- The stationary part of the tidal field is a DC effect, and simply adds to the stationary tidal forces
of all other objects in the universe. It is not possible to discriminate one source from another.
Gravitational waves carry time-dependent tidal forces, and so they can be discriminated from
the stationary field if one knows what kind of time dependence to look for. Interferometers are
ideal detectors in this respect because they sense only changes in the position of an interference
fringe, which makes them insensitive to the DC part of the tidal field.
Because gravitational waves couple so weakly to our detectors, those astronomical sources that we can
detect must be extremely luminous in gravitational radiation. Even at the distance of the Virgo
cluster of galaxies, a detectable source could be as luminous as the full Moon, if only for a
millisecond! Indeed, while radio astronomers deal with flux levels of Jy, mJy and even
Jy, in the
case of gravitational wave sources we encounter fluxes that are typically 1020 Jy or larger.
Gravitational wave astronomy therefore is biased toward looking for highly energetic, even catastrophic,
events.
Extracting useful physical, astrophysical and cosmological information from gravitational wave
observations is made possible by measuring a number of gravitational wave attributes that are related to
the properties of the source. In the rest of this section we discuss those attributes of gravitational radiation
that can be measured via gravitational wave observations. In the process we will review the basic formulas
used in computing the gravitational wave amplitude and luminosity of a source. These will then be used in
Section 3 to make an order-of-magnitude estimate of the strength of astronomical sources of gravitational
waves.