Effects of Gravitational Radiation Reaction in the General Relativistic Two-Body Problem by a Lorentz-Invariant Approximation Method

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Abstract
A Lorentz-invariant approximation method for obtaining the equations of motion of mass points in the general theory of relativity was developed recently. If retarded interactions are assumed, the first-order equations contain radiation reaction terms similar to those appearing in electrodynamics. These equations are used to investigate the question of the existence of gravitational radiation through the examination of selected approximate solutions of the two-body problem, without recourse to the assumption of slow motion. For the case of equal masses, the motion is almost circular; the particles are found to spiral outward in time. This result is in disagreement with Einstein's calculation of the distant field and the resulting energy loss due to quadrupole radiation based on the linear approximation, which, however, did not take proper account of the motion of the particles consistent with the approximate field equations used. These equations lead in a natural manner to an energy-momentum pseudotensor of the field consistent with the approximate equations of motion employed here. Using this pseudotensor, the distant outgoing retarded field due to the circular motion of two equal masses is found to correspond to an energy influx of quadrupole type; similar results are found for elliptic motion of unequal masses in slow-motion approximation. On the other hand, the assumption of advanced interactions would lead to inward spiraling and an incoming field with energy outflow. The significance of these discomforting results is discussed; possible objections against the equations of motion used, the method of solution of these equations, or the interpretation of the solutions obtained are examined. The possibility that the calculation of radiation effects on the basis of the higher order equations of motion will yield results differing qualitatively from those obtained here in first order cannot be excluded.

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