Non-conservative gravitational equations

We propose a theory of gravity based on the interaction of the gauge field representing gravitation with a suitable vector ''substratum'' (physical 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 mathematical structures, the logical theory of systems, the categorial algebra and the Lie algebra. The coupling of gravity to the substratum implies the nonconservation of the energy-momentum tenser. The derivative coupling term is approximated to the first order, and a Schwarzschild-like solution of the corresponding nonconservative gravitational equations is obtained. It is shown that, in this approximation, the main effect of the new theory is to introduce an extra-mass term in the standard Schwarzschild metric. The application of such a result to perihelion shifts and light deflection yields results comparable to those obtained in General Relativity. Gravitational-wave solutions of the new equations are derived in the weak field approximation. It is shown that our nonconservative theory of gravity implies a cosmological model with a locally varying, non-zero cosmological ''constant''.