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Basic Notions

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

Abstract

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.

Keywords

Tangent Space Covariant Derivative Bianchi Identity Lorentz Group Minkowski Spacetime 
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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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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