Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2001-11-30
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Doctoral thesis, 142(+6) pages, 2 figures, LaTeX; v5: connection changed; v6: local conservation laws changed; v7: chapter 5 b
Scientific paper
In this thesis a non-standard geometric framework, the "quasi-metric" framework (QMF), is used to define relativistic space-time. The QMF consists of a 4-dimensional space-time manifold equipped with a one-parameter family of Lorentzian 4-metrics parameterized by a (unique) global time function. Equivalently the QMF may be described as a 4-dimensional submanifold of a 5-dimensional product manifold equipped with a degenerate metric, where the global time function represents one extra degenerate time dimension. A symmetric and linear connection compatible with the non-degenerate piece of the degenerate metric is defined, yielding equations of motion. These equations are identical to the geodesic equation obtained from the connection. The role of the degenerate dimension is to describe global scale changes between gravitational and non-gravitational systems. In particular this yields an alternative description of the expansion of the Universe. In this thesis a quasi-metric theory of gravity is constructed. The field equations have only one dynamical degree of freedom coupled explicitly to matter, but there is also a second, implicit dynamical degree of freedom. The existence of an implicit coupling 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. But the non-metric part of the theory may be tested rather independently. That is, the theory predicts that vacuum gravitational fields and gravitationally bound bodies made of ideal gas expand like the expansion of the Universe. Several observations suggest this; e.g. the "Pioneer effect", the spin-down of the Earth, palaeo-tidal records etc. Thus quasi-metric relativity has experimental support where metric theories fail.
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