Some Problems on Lorentz Manifolds

  • Yuri E. Gliklikh
Part of the Theoretical and Mathematical Physics book series (TMP)


In this Section we give a brief introduction to some core notions of relativity theory. This material suffices to understand the language of relativity and to describe the relativistic problems discussed below. We are mainly interested in the constructions of general relativity, the formulae of special relativity arising as consequences of the latter. Since the exposition is intended for mathematicians, we present it axiomatically, starting from a basic set of postulates. Such an approach allows us to focus on the mathematical background of general relativity and on the physical interpretation of the mathematical developments. We do not touch on the physical background, however it is used to motivate the above-mentioned postulates. We refer the reader to (Misner et al., 1973; Sachs and Wu, 1977) for details.


Black Hole Reference Frame Tangent Space Minkowski Space Light Cone 
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  1. 182.
    Misner, C., Thorne, K., Wheeler, J.: Gravitation. Freeman, N.Y. (1973) Google Scholar
  2. 200.
    Sachs, R.K., Wu, H.: General Relativity for Mathematicans. Springer-Verlag, N.Y. (1977) Google Scholar

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© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Mathematics DepartmentVoronezh State UniversityVoronezhRussia

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