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We define a Post Minkowskian iteration method for solving Einstein's vacuum equations and we give the general structure of the solution when r→o or c→+∞. The method is then used to derive an expression for the radiation force density in the case of a non-relativistic source.
The space of Cauchy data. for Einstein equations is effectively reduced with respect to Gauss-Codazzi constraints. The mixed initial value — boundary value problem is analysed. The role ofboundary degrees of freedom is discussed. The energy-positivity is obtained as a simple consequence of the construction used.
The bundle of principal connections of a principal bundle is used to study some stability problems in the theory of b-completions. It follows that b-incompleteness is stable under perturbations of the connection. This adds weight to the belief that general relativistic singularities cannot be removed by quantization.
It is shown that every Petrov type N space-time on which the conformally invariant scalar wave equation satisfies Huygens' principle is conformally related to a special complex recurrent space-time.
Space-curvature induced modifications of the electronic, fine and hyperfine structure energies and wavefunctions have been investigated when the usual Euclidean flat space is substituted by a spherical 3-space: Particularly, it has been found that the degenerate one-electron fine structure energy levels are split by an additionnal space-curvature contribution which vanishes at the traditional flat-space...
The postulates upon which is founded general relativity (in particular the principle of equivalence) are in fact the underlying foundations of a large class of competing theories, the so-called metric theories of gravity. This situation has led the physicists to propose and to perform two kinds of experiments: 1) experiments which test the pertinence of the concept of metric theory; 2) experiments...
We hope that this review has shown the works already achieved but also the investigations which have to be done, in a closer cooperation between theoreticians, geodesists and astronomes. It is surthat new effects are to be added soon at the survey done in this paper.
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