Conservation laws, symmetry properties, and the equivalence principle in aclass 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 wa s where the matter field Lagrangian density L-M does not depend on the conn ection. For this theory we derive an analogue of the Einstein pseudotensor and the von Freud superpotential. Then we derive, using the arbitrariness t hat is always present in the choice of pseudotensor and superpotential, a g eneralization of the Moller superpotential as associated with a double-inde x differential conservation law. This superpotential allows us to deduce th at there are two analogues of the Komar vector of general relativity (GR): one associated with the general connection and the other with the metric co nnection. Astonishingly both of them satisfy the physical condition that th e inertial mass must be equal to the gravitational (active) mass for any cl ass of matter. We also obtain a generalization of Tolman's expression for t he energy, and prove that those theories with f(0) = 0 share with GR the pr operty that the total energy is independent of any two-dimensional surface which encloses the support of the matter distribution. [S0556-2821(99)03614 -0].