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​ d t , with f(r) = 1-2GM/(r$c^2$) for Schwarzschild. A locally conserved (Killing) energy $E_\infty$ — the energy the same quantity would be assigned by a distant static observer — and the energy measured by the local static observer, $E_{\rm loc}$ , are related by the standard blueshift-on-the-way-down relation $E_{\rm loc} = \frac{E_\infty}{\sqrt{f(r)}}, \qquad\text{so that}\qquad E_{\rm loc}\,d\tau = E_\infty\,dt$. That second identity is the entire resolution in miniature, and it is worth deriving $N_\perp$[$\Gamma$] both ways to see it operate. Hold the local energy budget fixed at $E_{\rm loc}$=$E_0$' (a battery physically at the processor, delivering a fixed amount of locally measured energy) over a proper interval $\Delta$$\tau$ :

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