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Published equation contexts

Tij:=c2(ϕ,ij+ϕ,i ϕ,j)\mathcal T_{ij} := c^2\left(\phi_{,ij} + \phi_{,i}\,\phi_{,j}\right)

Why this formula appears here

Define the network’s curvature-diagnosing observable directly from this result, restoring physical units through the relation between coordinate acceleration and proper time for a static observer, Tij:=c2(ϕ,ij+ϕ,i ϕ,j)\mathcal T_{ij} := c^2\left(\phi_{,ij} + \phi_{,i}\,\phi_{,j}\right). a symmetric rank-two tensor in the local spatial frame of the static observers, with units of inverse time squared — the Eötvös units already standard in gravity-gradient surveying, where 1\,E\mathrm E = 10^{-9}\,s−2\mathrm{s^{-2}} . Under a rotation of the local spatial axes it transforms as an ordinary rank-two tensor; under a change of which node is used as the additive reference for ϕ\phi it is unchanged, because it depends only on derivatives of ϕ\phi , never its value; and up…

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ϕ,ij\phi_{,ij}

Symbol phi_,ij

phi_,ij is one of the signed contributions combined to compute the quantity on the left.

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Published contexts (1)

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Tij:=c2(ϕ,ij+ϕ,i ϕ,j),\mathcal T_{ij} := c^2\left(\phi_{,ij} + \phi_{,i}\,\phi_{,j}\right),

Equation 100 · Evolutionary Physics

The Bend an Elevator Cannot Fake

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

Define the network’s curvature-diagnosing observable directly from this result, restoring physical units through the relation between coordinate acceleration and proper time for a static observer, Tij:=c2(ϕ,ij+ϕ,i ϕ,j)\mathcal T_{ij} := c^2\left(\phi_{,ij} + \phi_{,i}\,\phi_{,j}\right). a symmetric rank-two tensor in the local spatial frame of the static observers, with units of inverse time squared — the Eötvös units already standard in gravity-gradient surveying, where 1\,E\mathrm E = 10^{-9}\,s−2\mathrm{s^{-2}} . Under a rotation of the local spatial axes it transforms as an ordinary rank-two tensor; under a change of which node is used as the additive reference for ϕ\phi it is unchanged, because it depends only on derivatives of ϕ\phi , never its value; and up…

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