NONCONSERVATIVE GRAVITATIONAL EQUATIONS

We propose a theory of gravity based on the interaction of the gauge f ield representing gravitation with a suitable vector ''substratum'' (p hysical vacuum). To build up the new theory, we exploit the formalism of the Symbolic Gauge Theory, an application to gauge theories of the General System Logic Theory, which results from the Fusion of three ma thematical structures, the logical theory of systems, the categorial a lgebra and the Lie algebra. The coupling of gravity to the substratum implies the nonconservation of the energy-momentum tenser. The derivat ive coupling term is approximated to the first order, and a Schwarzsch ild-like solution of the corresponding nonconservative gravitational e quations is obtained. It is shown that, in this approximation, the mai n effect of the new theory is to introduce an extra-mass term in the s tandard Schwarzschild metric. The application of such a result to peri helion shifts and light deflection yields results comparable to those obtained in General Relativity. Gravitational-wave solutions of the ne w equations are derived in the weak field approximation. It is shown t hat our nonconservative theory of gravity implies a cosmological model with a locally varying, non-zero cosmological ''constant''.