Quasi-Metric Relativity

Abstract

This is a survey of a new type of relativistic space-time framework; the so-called quasi-metric framework. The basic geometric structure underlying quasi-metric relativity is quasi-metric space-time; this is defined as a 4-dimensional differentiable manifold ${\cal N}$ equipped with two one-parameter families ${\bf {\bar g}}_t$ and ${\bf g}_t$ of Lorentzian 4-metrics parametrized by a global time function $t$. The metric family ${\bf {\bar g}}_t$ is found from field equations, whereas the metric family ${\bf g}_t$ is used to propagate sources and to compare predictions to experiments. A linear and symmetric affine connection compatible with the family ${\bf g}_t$ is defined, giving rise to equations of motion. Furthermore a quasi-metric theory of gravity, including field equations and local conservation laws, is presented. Just as for General Relativity, the field equations accommodate two independent propagating dynamical degrees of freedom. On the other hand, the particular structure of quasi-metric geometry allows only a partial coupling of space-time geometry to the active stress-energy tensor. Besides, the field equations are defined from projections of physical and geometrical tensors with respect to a ``preferred'' foliation of quasi-metric space-time into spatial hypersurfaces. The dynamical nature of this foliation makes the field equations unsuitable for a standard PPN-analysis. This implies that the experimental status of the theory is not completely clear at this point in time. The theory seems to be consistent with a number of cosmological observations and it satisfies all the classical solar system tests, though. Moreover, in its non-metric sector the new theory has experimental support where General Relativity fails or is irrelevant.Comment: 39 pages, no figures, LaTeX; v2: some points clarified; v3: connection changed; v4: extended and local conservation laws changed; v5: major revision; v6: accepted for publication in G&C; v7: must have non-universal gravitational coupling; v8: rewritten with fully coupled theory; v9: major revision (fully coupled theory abandoned