Equation 78 · Part 4 · The Bend an Elevator Cannot Fake

Symbol x

ds^2 = -U(\mathbf x)^2\,dx_0^2 + \delta_{ij}\,dx^i dx^j

x

What this part means

x is one of the signed contributions combined to compute the quantity on the left.

Its job in the formula

x is one of the signed contributions combined to compute the quantity on the left.

Full expressionSymbol xArticle meaning

The passage around this formula

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…

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the article section

[14] General Relativity ↗

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