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advanced_tools:connections:levi_civita_connection
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$ \Gamma_{ijk} \equiv -\bigl(\partial_{i}g_{jk}-\partial_{k}g_{ij}-\partial_{j}g_{ki}\bigr)$
Christoffel Symbols
Intuitive
Christoffel symbols $\Gamma^i_{jk}$ are a particular type of connection that a Lorentzian manifold has (called the Levi-Civita connection).
A connection is a tool that we use to parallel transport tangent vectors around the manifold.
Parallel transport is just the simplest way to compare vectors at different points in the manifold.
Parallel is necessary, for example, to define the covariant derivative.
Concrete
In this section things should be explained by analogy and with pictures and, if necessary, some formulas.
Abstract
The motto in this section is: the higher the level of abstraction, the better.
Why is it interesting?
The Christoffel symbols appear in the most important equations of general relativity: the Einstein equation and the geodesic equation.
advanced_tools/connections/levi_civita_connection.1523696612.txt.gz · Last modified: 2018/04/14 09:03 (external edit)
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