Equation 85 · Part 3 · The Bend an Elevator Cannot Fake

Symbol phi_,i

\partial_j(U^2\phi_{,i}) = U^2\phi_{,i}\phi_{,j} + U^2\phi_{,ij}

\phi_{,i}

What this part means

phi_,i is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

Its job in the formula

phi_,i is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

Full expressionSymbol phi_,iArticle meaning

The passage around this formula

…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…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the article section

[14] General Relativity ↗

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