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The primary purpose of all physical theory is rooted in reality, and most relativists pretend to be physicists. We may often be members of departments of mathematics and our work oriented towards the mathematical aspects of Einstein’s theory, but even those of us who hold a permanent position on “scri”, are primarily looking there for gravitational waves. Of course, the builder of this theory and...
Various aspects of the Cauchy problem for the Einstein equations are surveyed, with the emphasis on local solutions of the evolution equations. Particular attention is payed to giving a clear explanation of conceptual issues which arise in this context. The question of producing reduced systems of equations which are hyperbolic is examined in detail and some new results on that subject are presented...
Let us declare that the most important devoir of any physical theory is to draw firm predictions for the outcome of laboratory experiments and astronomical observations. Unfortunately, the devoir is quite difficult to fulfill in the case of general relativity, essentially because of the complexity of the Einstein field equations, to which only few exact solutions are known. For instance, it is impossible...
Duality is presently considered the key to the Holy Grail of String Theory— it is supposed to provide links between the five known different superstring theories in ten dimensions, hoped to be just different limits of one unique eleven dimensional theory [1]. The main role of duality is to relate two different regimes— e.g. one of weak and one of strong coupling— of these theories. In most cases duality...
In this article we want to describe what is known about time independent spacetimes from a global point of view. The physical situations we want to treat are isolated bodies at rest or in uniform rotation in an otherwise empty universe. In such cases one expects the gravitational field to have no “independent degrees of freedom”. Very loosely speaking, the spacetime geometry should be uniquely determined...
The theory of gravitational lensing is discussed in a Lorentzian manifold setting. To that end we fix a point ρ (observer at a particular instant) and a time- like curve γ (worldline of a light source) in a 4-dimensional Lorentzian manifold (spacetime) and we investigate how many past-pointing lightlike geodesics (light rays) go from ρ to γ. If there is more than one such geodesic, then we are in...
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