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Published equation contexts

N⊥=2πℏE0′ ΔτN_\perp = \frac{2}{\pi\hbar}E_0'\,\Delta\tau

Why this formula appears here

That second identity is the entire resolution in miniature, and it is worth deriving N⊥N_\perp[Γ\Gamma] both ways to see it operate. Hold the local energy budget fixed at ElocE_{\rm loc}=E0E_0' (a battery physically at the processor, delivering a fixed amount of locally measured energy) over a proper interval Δ\Deltaτ\tau : N⊥=2πℏE0′ ΔτN_\perp = \frac{2}{\pi\hbar}E_0'\,\Delta\tau. Now hold the asymptotic Killing energy fixed instead, at E∞E_\infty = f\sqrt{f}\,E0E_0' (the amount of energy it would cost a distant experimenter, at infinity, to deliver that same physical resource down to radius r ), and integrate over the corresponding coordinate interval Δ\Delta t = Δ\Deltaτ\tau/f\sqrt f :

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N⊥N_\perp

Symbol N_perp

NpN_perp is part of the quantity the equation computes from the expression on the right.

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π\pi

Symbol pi

pi occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

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How to interpret it

With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.

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Published contexts (1)

A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.

N⊥=2πℏE0′ Δτ.N_\perp = \frac{2}{\pi\hbar}E_0'\,\Delta\tau.

Equation 48 · Evolutionary Physics

A Horizon Is a Toll Booth, Not a Loophole

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

That second identity is the entire resolution in miniature, and it is worth deriving N⊥N_\perp[Γ\Gamma] both ways to see it operate. Hold the local energy budget fixed at ElocE_{\rm loc}=E0E_0' (a battery physically at the processor, delivering a fixed amount of locally measured energy) over a proper interval Δ\Deltaτ\tau : N⊥=2πℏE0′ ΔτN_\perp = \frac{2}{\pi\hbar}E_0'\,\Delta\tau. Now hold the asymptotic Killing energy fixed instead, at E∞E_\infty = f\sqrt{f}\,E0E_0' (the amount of energy it would cost a distant experimenter, at infinity, to deliver that same physical resource down to radius r ), and integrate over the corresponding coordinate interval Δ\Delta t = Δ\Deltaτ\tau/f\sqrt f :

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