A suitable array of gravitational antennas could delineate or
limit the number of modes present in a given wave. The strategy
depends on whether or not the source direction is known. In
general there are eight unknowns (six polarizations and two
direction cosines), but only six measurables (). If the direction can be established by either association of
the waves with optical or other observations, or by
time-of-flight measurements between separated detectors, then six
suitably oriented detectors suffice to determine all six
components. If the direction cannot be established, then the
system is underdetermined, and no unique solution can be found.
However, if one assumes that only transverse waves are present,
then there are only three unknowns if the source direction is
known, or five unknowns otherwise. Then the corresponding number
(three or five) of detectors can determine the polarization. If
distinct evidence were found of any mode other than the two
transverse quadrupolar modes of GR, the result would be
disastrous for GR. On the other hand, the absence of a breathing
mode would not necessarily rule out scalar-tensor gravity,
because the strength of that mode depends on the nature of the
source.
Some of the details of implementing such polarization
observations have been worked out for arrays of resonant
cylindrical, disk-shaped, spherical and truncated icosahedral
detectors (TEGP 10.2 [147], for recent reviews see [87,
133]); initial work has been done to assess whether the ground-based
or space-based laser interferometers (or combinations of the two
types) could perform interesting polarization measurements [134,
33,
90,
67]. Unfortunately for this purpose, the two LIGO observatories (in
Washington and Louisiana states, respectively) have been
constructed to have their respective arms as parallel as
possible, apart from the curvature of the Earth; while this
maximizes the joint sensitivity of the two detectors to
gravitational waves, it minimizes their ability to detect two
modes of polarization.
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The Confrontation between General Relativity and
Experiment
Clifford M. Will http://www.livingreviews.org/lrr-2001-4 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de |