Symbol f

The passage around this formula

Staying 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 required clearance gives $\Delta$ r$\approx$2.8$\times$10^{-14}\,$\mathrm m$ — a few nuclear radii from the horizon. For a supermassive hole, in other words, the ambient Hawking bath…

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