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The 4D Spacetime

  • Carles BonaEmail author
  • Carles Bona-Casas
  • Carlos Palenzuela-Luque
Chapter
Part of the Lecture Notes in Physics book series (LNP, volume 783)

Physics theories are made by building mathematical models that correspond to physical systems. General relativity, the physical theory of gravitation, models spacetime in a geometrical way: as a 4D manifold. The concept of manifold is just a generalization to the multidimensional case of the usual concept of a 2D surface. This will allow us to apply the well-known tools of differential geometry, the branch of mathematics which describes surfaces, to the study of spacetime geometry.

Keywords

Curvature Tensor Bianchi Identity Principal Part Energy Tensor Spacetime Geometry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    H. Stephani et al. Exact Solutions of Einstein’s Field Equations, 2nd edn, Cambridge, Cambridge New York (2003)zbMATHCrossRefGoogle Scholar
  2. 2.
  3. 3.
  4. 4.
    T. De Donder, La Gravifique Einstenienne, Gauthier-Villars, Paris (1921).Google Scholar
  5. 5.
    T. De Donder, The Mathematical Theory of Relativity, Massachusetts Institute of Technology, Cambridge (1927).zbMATHGoogle Scholar
  6. 6.
    K. Lanczos, Ann. Phys. 13, 621 (1922).Google Scholar
  7. 7.
    K. Lanczos, Z. Phys. 23, 537 (1923).Google Scholar
  8. 8.
    V. A. Fock, The Theory of Space, Time and Gravitation, Pergamon, London (1959).zbMATHGoogle Scholar
  9. 9.
    Y. Choquet (Fourès)-Bruhat, Acta Matematica 88, 141 (1952).CrossRefGoogle Scholar
  10. 10.
    Y. Choquet (Fourès)-Bruhat, ‘Cauchy problem’ in Gravitation: An Introduction to Current Research, ed. by L. Witten, Wiley, New York (1962).Google Scholar
  11. 11.
    H. Friedrich, Commun. Math. Phys. 100, 525 (1985).zbMATHCrossRefADSMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Carles Bona
    • 1
    Email author
  • Carles Bona-Casas
    • 1
  • Carlos Palenzuela-Luque
    • 2
  1. 1.Departament de FísicaUniversitat de les Illes BalearsPalma de MallorcaSpain
  2. 2.Max-Planck-Institut für Gravitationsphysik (Albert Einstein Institut)GolmGermany

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