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Equation 41 · Part 2 · A Horizon Is a Toll Booth, Not a Loophole

Symbol r

f(r)=1−2GM/(rc2)f(r) = 1-2GM/(rc^2)
rr

What this part means

r is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

Its job in the formula

r is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

The passage around this formula

​ d t , with f(r) = 1-2GM/(rc2c^2) for Schwarzschild. A locally conserved (Killing) energy E∞E_\infty — the energy the same quantity would be assigned by a distant static observer — and the energy measured by the local static observer, ElocE_{\rm loc} , are related by the standard blueshift-on-the-way-down relation

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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