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 GR, 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
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 GR, 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 GR, 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
. Thus, despite the presence of dipole gravitational radiation, the binary pulsar
provides at present only a weak test of Brans-Dicke theory, not competitive with solar-system
tests.
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