An Einstein-Hilbert Action for Axi-Dilaton Gravity in 4-Dimensions

We examine the axi-dilatonic sector of low energy string theory and demonstrate how the gravitational interactions involving the axion and dilaton fields may be derived from a geometrical action principle involving the curvature scalar associated with a non-Riemannian connection. In this geometry the antisymmetric tensor 3-form field determines the torsion of the connection on the frame bundle while the gradient of the metric is determined by the dilaton field. By expressing the theory in terms of the Levi-Civita connection associated with the metric in the ``Einstein frame'' we confirm that the field equations derived from the non-Riemannian Einstein-Hilbert action coincide with the axi-dilaton sector of the low energy effective action derived from string theory.Comment: 6 pages Plain Tex (No Figures), Letter to Editor Classical and Quantum Gravit

Non-Riemannian Gravity and the Einstein-Proca System

We argue that all Einstein-Maxwell or Einstein-Proca solutions to general relativity may be used to construct a large class of solutions (involving torsion and non-metricity) to theories of non-Riemannian gravitation that have been recently discussed in the literature.Comment: 9 pages Plain Tex (No Figures), Letter to Editor Classical and Quantum Gravit

Black Holes with Weyl Charge and Non-Riemannian Waves

A simple modification to Einstein's theory of gravity in terms of a non-Riemannian connection is examined. A new tensor-variational approach yields field equations that possess a covariance similar to the gauge covariance of electromagnetism. These equations are shown to possess solutions analogous to those found in the Einstein-Maxwell system. In particular one finds gravi-electric and gravi-magnetic charges contributing to a spherically symmetric static Reissner-Nordstr\"om metric. Such Weyl ``charges'' provide a source for the non-Riemannian torsion and metric gradient fields instead of the electromagnetic field. The theory suggests that matter may be endowed with gravitational charges that couple to gravity in a manner analogous to electromagnetic couplings in an electromagnetic field. The nature of gravitational coupling to spinor matter in this theory is also investigated and a solution exhibiting a plane-symmetric gravitational metric wave coupled via non-Riemannian waves to a propagating spinor field is presented.Comment: 18 pages Plain Tex (No Figures), Classical and Quantum Gravit

Dark Matter Gravitational Interactions

We argue that the conjectured dark mater in the Universe may be endowed with a new kind of gravitational charge that couples to a short range gravitational interaction mediated by a massive vector field. A model is constructed that assimilates this concept into ideas of current inflationary cosmology. The model is also consistent with the observed behaviour of galactic rotation curves according to Newtonian dynamics. The essential idea is that stars composed of ordinary (as opposed to dark matter) experience Newtonian forces due to the presence of an all pervading background of massive gravitationally charged cold dark matter. The novel gravitational interactions are predicted to have a significant influence on pre-inflationary cosmology. The precise details depend on the nature of a gravitational Proca interaction and the description of matter. A gravitational Proca field configuration that gives rise to attractive forces between dark matter charges of like polarity exhibits homogeneous isotropic eternal cosmologies that are free of cosmological curvature singularities thus eliminating the horizon problem associated with the standard big-bang scenario. Such solutions do however admit dense hot pre-inflationary epochs each with a characteristic scale factor that may be correlated with the dark matter density in the current era of expansion. The model is based on a theory in which a modification of Einsteinian gravity at very short distances can be expressed in terms of the gradient of the Einstein metric and the torsion of a non-Riemannian connection on the bundle of linear frames over spacetime. Indeed we demonstrate that the genesis of the model resides in a remarkable simplification that occurs when one analyses the variational equations associated with a broad class of non-Riemannian actions.Comment: 40 pages, 4 Postscript figure