In mathematics and physics, the Christoffel symbols are an array of numbers describing a metric connection. The metric connection is a specialization...
42 KB (7,076 words) - 16:07, 8 July 2024
Contracted Bianchi identities (redirect from Christoffel symbols/Proofs)
In general relativity and tensor calculus, the contracted Bianchi identities are: ∇ ρ R ρ μ = 1 2 ∇ μ R {\displaystyle \nabla _{\rho }{R^{\rho }}_{\mu...
4 KB (615 words) - 00:14, 13 May 2024
Elwin Bruno Christoffel (German: [kʁɪˈstɔfl̩]; 10 November 1829 – 15 March 1900) was a German mathematician and physicist. He introduced fundamental concepts...
11 KB (1,148 words) - 09:29, 20 August 2024
Levi-Civita connection (section Christoffel symbols)
called Christoffel symbols. The Levi-Civita connection is named after Tullio Levi-Civita, although originally "discovered" by Elwin Bruno Christoffel. Levi-Civita...
21 KB (3,392 words) - 15:10, 28 September 2024
Reissner–Nordström metric (section Christoffel symbols)
{\displaystyle v_{\rm {esc}}={\frac {\sqrt {\gamma ^{2}-1}}{\gamma }}.} The Christoffel symbols Γ j k i = ∑ s = 0 3 g i s 2 ( ∂ g j s ∂ x k + ∂ g s k ∂ x j − ∂...
19 KB (3,490 words) - 00:30, 3 September 2024
except when noted otherwise. In a smooth coordinate chart, the Christoffel symbols of the first kind are given by Γ k i j = 1 2 ( ∂ ∂ x j g k i + ∂...
20 KB (5,396 words) - 16:29, 11 October 2024
Ricci and Levi-Civita (following ideas of Elwin Bruno Christoffel) observed that the Christoffel symbols used to define the curvature could also provide a...
37 KB (6,473 words) - 00:23, 24 September 2024
the covariant derivative can be written in terms of Christoffel symbols. The Christoffel symbols find frequent use in Einstein's theory of general relativity...
27 KB (3,174 words) - 02:46, 7 September 2024
Schwarzschild geodesics (section Christoffel symbols)
{\frac {6\pi G(M+m)}{c^{2}A\left(1-e^{2}\right)}}} The non-vanishing Christoffel symbols for the Schwarzschild-metric are: Γ r t t = − Γ r r r = r s 2 r (...
65 KB (12,016 words) - 21:35, 2 October 2024
Differential geometry of surfaces (section Christoffel symbols, Gauss–Codazzi equations, and the Theorema Egregium)
the Christoffel symbols as coordinates of the second partial derivatives of f. The choice of unit normal has no effect on the Christoffel symbols, since...
128 KB (17,447 words) - 23:59, 27 September 2024