Einstein’s Equations

  • Dieter LüstEmail author
  • Ward Vleeshouwers
Part of the SpringerBriefs in Physics book series (SpringerBriefs in Physics)


The Christoffel connection is associated to a covariant derivative acting on tensors. In familiar gauge theories, the partial derivative is replaced by a covariant derivative as \(\partial _{\mu } \rightarrow D_{\mu } = \partial _{\mu }+ ie A_{\mu }(x)\). In general relativity, the covariant derivative acts as \(\partial _{\mu } \rightarrow \nabla _{\mu } = \left( \partial _{\mu }+ \Gamma ^{\nu }_{\mu \lambda }\right) \circ \), where \(\circ \) indicates that multiplication is tensorially non-trivial, see ( 4.2).

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© The Author(s), under exclusive license to Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Arnold-Sommerfeld-CenterLudwig-Maximilians-UniversitaetMunichGermany
  2. 2.Institute for Theoretical PhysicsUtrecht UniversityUtrechtThe Netherlands

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