Published equation contexts

$\mathcal T_{ij} \equiv 0$

Why this formula appears here

Two known limits anchor it. First, the elevator: $\mathcal T_{ij}$ $\equiv$ 0 for any uniformly accelerated frame, proven directly above — the “uniform potential difference is not curvature” claim, derived rather than asserted. Second, weak-field gravity: expanding $\phi$ $\approx$ $\Phi$ / $c^2$ for small $\Phi$ / $c^2$ , the quadratic term $\phi_{,i}$ $\phi_{,j}$ is second order in the already-small ratio $\Phi$ / $c^2$ and negligible next to the first-order term $\phi_{,ij}$ $\approx$ $\Phi_{,ij}$ / $c^2$ , so $\mathcal T_{ij}$ $\to$ $\Phi_{,ij}$ , exactly the ordinary Newtonian tidal tensor of tower and satellite geodesy [ 15 , 14 ] . The first derivative alone, meanwhile, recovers the textbook gravitational redshift these networks…

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T_{ij}

Symbol T_ij

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\mathcal T_{ij} \equiv 0

Equation 108 · Evolutionary Physics

The Bend an Elevator Cannot Fake

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

Two known limits anchor it. First, the elevator: $\mathcal T_{ij}$ $\equiv$ 0 for any uniformly accelerated frame, proven directly above — the “uniform potential difference is not curvature” claim, derived rather than asserted. Second, weak-field gravity: expanding $\phi$ $\approx$ $\Phi$ / $c^2$ for small $\Phi$ / $c^2$ , the quadratic term $\phi_{,i}$ $\phi_{,j}$ is second order in the already-small ratio $\Phi$ / $c^2$ and negligible next to the first-order term $\phi_{,ij}$ $\approx$ $\Phi_{,ij}$ / $c^2$ , so $\mathcal T_{ij}$ $\to$ $\Phi_{,ij}$ , exactly the ordinary Newtonian tidal tensor of tower and satellite geodesy [ 15 , 14 ] . The first derivative alone, meanwhile, recovers the textbook gravitational redshift these networks…

Equation guide → · Article →

Tij≡0\mathcal T_{ij} \equiv 0Tij​≡0