Tetrad (general theory of relativity)

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A tetrad (also called four-legged) is a method of calculating the curvature of space-time in general relativity . Instead of a coordinate base, a nonholonomic orthonormal base is used for the tangent space , so that the base vectors are orthonormal, i.e. their inner product ${\displaystyle \left\{e_{a}\right\}}$

${\displaystyle e_{\mu }\cdot e_{\nu }=\eta _{\mu \nu }}$

corresponds to the metric of the Minkowski space .

With the help of the Cartan structural equations, the curvature tensor can then be calculated.

literature

• Robert M. Wald : General Relativity. University of Chicago Press, 1984, ISBN 0-226-87033-2 .
• Mikio Nakahara: differential geometry, topology and physics. Springer Verlag, Berlin / Heidelberg, 2015, ISBN 978-3-662-45299-8 .