Conservation laws, symmetry properties, and the equivalence principle in a class of alternative theories of gravity -: art. no. 044012

We consider a subclass of alternative theories of gravitation obtained by a first order formalism from a Lagrangian density L-T = f(R) root-g + L-M was where the matter field Lagrangian density L-M does not depend on the connection. For this theory we derive an analogue of the Einstein pseudotensor and the von Freud superpotential. Then we derive, using the arbitrariness that is always present in the choice of pseudotensor and superpotential, a generalization of the Moller superpotential as associated with a double-index differential conservation law. This superpotential allows us to deduce that there are two analogues of the Komar vector of general relativity (GR): one associated with the general connection and the other with the metric connection. Astonishingly both of them satisfy the physical condition that the inertial mass must be equal to the gravitational (active) mass for any class of matter. We also obtain a generalization of Tolman's expression for the energy, and prove that those theories with f(0) = 0 share with GR the property that the total energy is independent of any two-dimensional surface which encloses the support of the matter distribution. [S0556-2821(99)03614-0].