Published equation contexts

$-\Gamma^i_{0\lambda}\Gamma^\lambda_{j0}$

Why this formula appears here

What must therefore vanish, identically, is not the slope but the correctly defined curvature-frame component built from it. For any static metric of the form d $s^2$ = -U( $\mathbf x$ )^2\,d $x_0^2$ + $\delta_{ij}$ \,d $x^i$ d $x^j$ — flat spatial slices, all the position dependence carried by U — the only nonzero Christoffel symbols are $\Gamma^0_{0i}$ = $\partial_i$ $\ln$ U = $\phi_{,i}$ and $\Gamma^i_{00}$ = $U^2$ $\phi_{,i}$ , both following directly from the metric’s definition. Substituting into the Riemann tensor’s defining combination for the mixed component $R^i$ {}_{0j0} , every term built from purely spatial Christoffels vanishes because the spatial slices are exactly flat, and the two surviving pieces are…

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\Gamma^i_{0\lambda}

Symbol Gamma^i_0λ

Gamm $a^i_0$ λ is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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\Gamma^\lambda_{j0}

Symbol Gamma^lambda_j0

Gamm $a^l$ ambd $a_j$ 0 is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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Research cited beside this formula

[14] General Relativity ↗

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-\Gamma^i_{0\lambda}\Gamma^\lambda_{j0}

Equation 84 · Evolutionary Physics

The Bend an Elevator Cannot Fake

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

What must therefore vanish, identically, is not the slope but the correctly defined curvature-frame component built from it. For any static metric of the form d $s^2$ = -U( $\mathbf x$ )^2\,d $x_0^2$ + $\delta_{ij}$ \,d $x^i$ d $x^j$ — flat spatial slices, all the position dependence carried by U — the only nonzero Christoffel symbols are $\Gamma^0_{0i}$ = $\partial_i$ $\ln$ U = $\phi_{,i}$ and $\Gamma^i_{00}$ = $U^2$ $\phi_{,i}$ , both following directly from the metric’s definition. Substituting into the Riemann tensor’s defining combination for the mixed component $R^i$ {}_{0j0} , every term built from purely spatial Christoffels vanishes because the spatial slices are exactly flat, and the two surviving pieces are…

Equation guide → · Article →

−Γ0λiΓj0λ-\Gamma^i_{0\lambda}\Gamma^\lambda_{j0}−Γ0λi​Γj0λ​