Basic Notions

  • Ruben Aldrovandi
  • José Geraldo Pereira
Part of the Fundamental Theories of Physics book series (FTPH, volume 173)


A general spacetime is a 4-dimensional differentiable manifold whose tangent space is, at each point, a Minkowski spacetime. Linear frames and tetrad fields are constitutive parts of its structure as a manifold, and instrumental in relativistic physics and gravitation. They are defined up to point-dependent Lorentz transformations, under which usual derivatives exhibit a non-covariance that can be just compensated by the non-covariance of connections, objects thereby essential to produce meaningful, covariant derivatives. Each connection defines a covariant derivative, from which two basic covariant objects result: curvature and torsion. These quantities satisfy two mandatory relations, the Bianchi identities.


Tangent Space Covariant Derivative Bianchi Identity Lorentz Group Minkowski Spacetime 
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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Ruben Aldrovandi
    • 1
  • José Geraldo Pereira
    • 1
  1. 1.Instituto de Física TeóricaUniversidade Estadual PaulistaSão PauloBrazil

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