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Eloc=E∞/fE_{\rm loc}=E_\infty/\sqrt f

Why this formula appears here

Rotating (Kerr) holes complicate the static-observer story: inside the ergosphere, no observer can remain static relative to infinity at all, and a locally nonrotating (ZAMO) observer is instead dragged around the hole at an angular rate fixed by the metric, with a redshift-like relation between locally measured and asymptotic energy that generalizes ElocE_{\rm loc}=E∞E_\infty/f\sqrt f to the appropriate lapse function of Boyer-Lindquist coordinates [ 13 ] . The ergosphere is also where the Penrose process operates: a particle split inside the ergosphere can send one fragment outward carrying more energy than the original particle possessed, with the deficit paid by the hole’s own rotational…

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ElocE_{\rm loc}

Symbol E_rm loc

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

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Eloc=E∞/fE_{\rm loc}=E_\infty/\sqrt f

Equation 88 · 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.

Rotating (Kerr) holes complicate the static-observer story: inside the ergosphere, no observer can remain static relative to infinity at all, and a locally nonrotating (ZAMO) observer is instead dragged around the hole at an angular rate fixed by the metric, with a redshift-like relation between locally measured and asymptotic energy that generalizes ElocE_{\rm loc}=E∞E_\infty/f\sqrt f to the appropriate lapse function of Boyer-Lindquist coordinates [ 13 ] . The ergosphere is also where the Penrose process operates: a particle split inside the ergosphere can send one fragment outward carrying more energy than the original particle possessed, with the deficit paid by the hole’s own rotational…

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