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Equation 41 · Part 6 · A Horizon Is a Toll Booth, Not a Loophole

=

f(r)=1−2GM/(rc2)f(r) = 1-2GM/(rc^2)
=

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

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

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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