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Equation 73 · Part 1 · A Horizon Is a Toll Booth, Not a Loophole

Symbol T_rm loc

Tloc(r)=TH/f(r)T_{\rm loc}(r)=T_H/\sqrt{f(r)}
TlocT_{\rm loc}

What this part means

TrT_rm loc is part of the quantity the equation computes from the expression on the right.

Its job in the formula

TrT_rm loc is part of the quantity the equation computes from the expression on the right.

The passage around this formula

…is THT_H=ℏ\hbar c3c^3/(8π\pi GMkBk_B)≈\approx1.5×\times10^{-14}\,K\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, Tloc(r)T_{\rm loc}(r)=THT_H/f(r)\sqrt{f(r)} [ 11 ] . Setting TlocT_{\rm loc} equal to a demanding but realistic dilution-refrigerator base temperature of 10\,mK\mathrm{mK} and solving for the required clearance gives Δ\Delta r≈\approx2.8×\times10^{-14}\,m\mathrm m — a few nuclear radii from the horizon. For a…

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