Equation 41 · A Horizon Is a Toll Booth, Not a Loophole
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
Read it piece by piece
Symbol f
f is part of the quantity the equation computes from the expression on the right.
Symbol r
r is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.
Symbol G
G is one of the signed contributions combined to compute the quantity on the left.
Symbol M
M is one of the signed contributions combined to compute the quantity on the left.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →superscript
A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.
See an illustrated explanation →How to interpret it
Read it with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
d t , with f(r) = 1-2GM/(r) for Schwarzschild. A locally conserved (Killing) energy — the energy the same quantity would be assigned by a distant static observer — and the energy measured by the local static observer, , are related by the standard blueshift-on-the-way-down relation
For background, read the article’s source list.
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