MODEL OF A SPINNING BODY WITHOUT GRAVITATIONAL RADIATION

A massive body with three mutually perpendicular planes of symmetry spins with constant angular velocity about an axis lying in two of these planes. Outside the body and concentric with it, there is a massive spherical shell. There is a vacuum between the body and the shell, and also outside the shell. The purpose of this paper is to construct a relativistic model to represent this situation. This is done by using a method of successive approximations to obtain a metric and an energy tensor in such a way that Einstein's field equations are satisfied to any desired degree of approximation, with the energy tensor = 0 in the vacuum domains and with positive density in the body and in the shell. There are two essential features of the method: (1) where d'Alembert's equation is to be solved, we use an equal mixture of retarded and advanced potentials, and (2) the metric outside the shell is made stationary at each step of the process by taking time-averages. The body is given the symmetry mentioned above, and is made to spin with constant angular velocity, in order to satisfy integrability conditions for certain partial differential equations. The same method can be used for a model in which the body does not rotate, but pulsates periodically, maintaining three mutually perpendicular planes of symmetry. In these models the field outside the shell is stationary and there is no gravitational radiation. On account of the assumed periodicity, there is no secular transfer of energy from the massive body to the spherical shell. (Author)
Revision of Report dated 28 Aug 67.