Equation 51 · 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 Δ t
Δ t is part of the quantity the equation computes from the expression on the right.
Symbol Δτ
Δτ is an input to the expression that computes the quantity on the left.
Symbol f
f is an input to the expression that computes the quantity on the left.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →change
Capital delta attached to a quantity marks a difference between two values of that quantity; the article’s sign convention determines the order.
How to interpret it
Read it with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
E 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 t = / :
For background, read the article’s source list.
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