In mathematics and physics, the Christoffel symbols are an array of numbers describing a metric connection. The metric connection is a specialization...

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...

Elwin Bruno Christoffel (German: [kʁɪˈstɔfl̩]; 10 November 1829 – 15 March 1900) was a German mathematician and physicist. He introduced fundamental concepts...

called Christoffel symbols. The Levi-Civita connection is named after Tullio Levi-Civita, although originally "discovered" by Elwin Bruno Christoffel. Levi-Civita...

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 + ∂...

Ricci and Levi-Civita (following ideas of Elwin Bruno Christoffel) observed that the Christoffel symbols used to define the curvature could also provide a...

the covariant derivative can be written in terms of Christoffel symbols. The Christoffel symbols find frequent use in Einstein's theory of general relativity...

{\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 − ∂...

{\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 (...

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...