Matter Creation or Destruction in a Variable Gravitational Field as Predicted by a Scalar Theory of Gravitation

Newton's second law: "force = time-derivative of momentum", may also be defined for theories of gravitation endowing space-time with a curved metric. Thus, Einstein's assumption of a geodesic motion may be rewritten in that form, and it corresponds to a velocity-dependent gravity acceleration vector g. In contrast, the investigated theory states that, in the preferred reference frame assumed by the theory, vector g does not depend on the velocity. It recovers geodesic motion only for a constant gravitational field. This leads to a different equation for continuum dynamics, as compared with general relativity. For a perfect fluid, this alternative dynamics predicts tenuous amounts of matter production or destruction, by a reversible exchange with the gravitational field. This exchange is completely determined by the dynamical equation and the scalar equation of the gravitational field. In contrast, the usual equation for relativistic continuum dynamics allows matter production only if some additional field is assumed, and the production rate must be phenomenologically postulated. With the alternative equation, the mass conservation is very nearly recovered for a weak field. The explosion (implosion) of a spherical compact body implies some matter production (destruction).