In another respect, however, the system has only partially
lived up to its promise, namely as a direct testing ground for
alternative theories of gravity. The origin of this promise was
the discovery that alternative theories of gravity generically
predict the emission of dipole gravitational radiation from
binary star systems. In general relativity, there is no dipole
radiation because the ``dipole moment'' (center of mass) of
isolated systems is uniform in time (conservation of momentum),
and because the ``inertial mass'' that determines the dipole
moment is the same as the mass that generates gravitational waves
(SEP). In other theories, while the inertial dipole moment may
remain uniform, the ``gravity wave'' dipole moment need not,
because the mass that generates gravitational waves depends
differently on the internal gravitational binding energy of each
body than does the inertial mass (violation of SEP).
Schematically, in a coordinate system in which the center of
inertial mass is at the origin, so that
, the dipole part of the retarded gravitational field would be
given by
where
and
and
m
are defined using inertial masses. In theories that violate SEP,
the difference between gravitational wave mass and inertial mass
is a function of the internal gravitational binding energy of the
bodies. This additional form of gravitational radiation damping
could, at least in principle, be significantly stronger than the
usual quadrupole damping, because it depends on fewer powers of
the orbital velocity
v, and it depends on the gravitational binding energy per unit
mass of the bodies, which, for neutron stars, could be as large
as 40 percent (see TEGP 10 [147
] for further details). As one fulfillment of this promise, Will
and Eardley worked out in detail the effects of dipole
gravitational radiation in the bimetric theory of Rosen, and,
when the first observation of the decrease of the orbital period
was announced in 1979, the Rosen theory suffered a terminal blow.
A wide class of alternative theories also fails the binary pulsar
test because of dipole gravitational radiation (TEGP 12.3 [147
]).
On the other hand, the early observations of PSR 1913+16
already indicated that, in GR, the masses of the two bodies were
nearly equal, so that, in theories of gravity that are in some
sense ``close'' to GR, dipole gravitational radiation would not
be a strong effect, because of the apparent symmetry of the
system. The Rosen theory, and others like it, are not ``close''
to general relativity, except in their predictions for the
weak-field, slow-motion regime of the solar system. When
relativistic neutron stars are present, theories like these can
predict strong effects on the motion of the bodies resulting from
their internal highly relativistic gravitational structure
(violations of SEP). As a consequence, the masses inferred from
observations of the periastron shift and
may be significantly different from those inferred using general
relativity, and may be different from each other, leading to
strong dipole gravitational radiation damping. By contrast, the
Brans-Dicke theory is ``close'' to GR, roughly speaking within
of the predictions of the latter, for large values of the
coupling constant
(here we use the subscript BD to distinguish the coupling
constant from the periastron advance
). Thus, despite the presence of dipole gravitational radiation,
the binary pulsar provides at present only a weak test of
Brans-Dicke theory, not yet competitive with solar-system
tests.
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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 |