What does this equation mean?

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 stays colder than any laboratory cryostat until the processor is closer to the horizon than an atomic nucleus, twenty-odd orders of magnitude closer than the point at which the support-acceleration bill already becomes unpayable. Cooling is a genuine, non-negotiable line item — it is what ties this construction to horizon thermodynamics at all — but for this mass scale it is not the item that kills the claim; the strut rig fails first, by an enormous margin.