Titlebook: Spacetime; Foundations of Gener Marcus Kriele Book 1999 Springer-Verlag Berlin Heidelberg 1999 Causality.Cosmology.Gravitation.Relativity.S

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questions on the all-important United States Medical Licensing Examination. Roger A. Brumback Richard W. Leech Acknowledgments This text would not have been po978-0-387-94389-3978-1-4612-0811-2Series ISSN 1431-6013

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0940-7677 hematical theories have had concept. Physical an especially the important on of and impact development mathematics, conversely various modern theories physical rather require sophisticated mathem- ics978-3-642-08564-2978-3-540-48354-0Series ISSN 0940-7677

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978-3-642-08564-2Springer-Verlag Berlin Heidelberg 1999

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Analysis on manifolds,Special relativity can only be expected to be a good description locally. We will assume that special relativity is an exact “infinitesimal” description, i.e. that it holds as a first order approximation near any given point. A rigorous formulation of this idea requires manifolds and tensor fields which will be introduced in this chapter.

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General relativity,Einstein’s equation is of the form ., where . is an operator acting on the Lorentzian metric . and . an expression which describes the distribution of matter in the universe. In Sect. 5.1 we motivate that . should be a symmetric . tensor field which is divergence-free, 2 and in Sect. 5.3 we find an expression for ..

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Causality,In this chapter we link the concept of causality to the conformal structure induced by the metric and present some elementary causal properties and their interpretation.

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