Introduction to the mathematics of general relativity: Difference between revisions

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===Christoffel symbols===

{{main|Christoffel symbolsymbols}}

The equation for the covariant derivative can be written in terms of Christoffel symbols. The Christoffel symbols find frequent use in Einstein's theory of [[general relativity]], where [[spacetime]] is represented by a curved 4-dimensional [[Lorentz manifold]] with a [[Levi-Civita connection]]. The [[Einstein field equations]] – which determine the geometry of spacetime in the presence of matter – contain the [[Ricci tensor]]. Since the Ricci tensor is derived from the Riemann curvature tensor, which can be written in terms of Christoffel symbols, a calculation of the Christoffel symbols is essential. Once the geometry is determined, the paths of particles and light beams are calculated by [[solving the geodesic equations]] in which the Christoffel symbols explicitly appear.