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  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 ).
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.
|The Confrontation between General Relativity and
Clifford M. Will
© Max-Planck-Gesellschaft. ISSN 1433-8351
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