Equation 72 · Part 1 · A Horizon Is a Toll Booth, Not a Loophole

Symbol r

r

r

What this part means

the radius.

Its job in the formula

r is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Full expressionSymbol rArticle meaning

Where the article explains it

A static observer at radius r sees this blueshifted by the same Tolman factor that governs any locally measured temperature in a static spacetime, $T_{\rm loc}(r)$ = $T_H$ / $\sqrt{f(r)}$ [ 11 ] .

The passage around this formula

…cold is the second cost, and here the numbers run the other way. The Hawking temperature of Sagittarius A* at infinity is $T_H$ = $\hbar$ $c^3$ /(8 $\pi$ GM $k_B$ ) $\approx$ 1.5 $\times$ 10^{-14}\, $\mathrm K$ [ 10 ] . A static observer at radius r sees this blueshifted by the same Tolman factor that governs any locally measured temperature in a static spacetime, $T_{\rm loc}(r)$ = $T_H$ / $\sqrt{f(r)}$ [ 11 ] . Setting $T_{\rm loc}$ equal to a demanding but realistic dilution-refrigerator base temperature of 10\, $\mathrm{mK}$ and solving for the…

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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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Sources cited in the surrounding passage

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