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Published equation contexts

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

Why this formula appears here

Staying cold is the second cost, and here the numbers run the other way. The Hawking temperature of Sagittarius A* at infinity 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 supermassive hole, in other words, the ambient Hawking bath…

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TlocT_{\rm loc}

Symbol T_rm loc

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

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

Equation 73 · Evolutionary Physics

A Horizon Is a Toll Booth, Not a Loophole

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

Staying cold is the second cost, and here the numbers run the other way. The Hawking temperature of Sagittarius A* at infinity 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 supermassive hole, in other words, the ambient Hawking bath…

Meanings in this article

  • rr: the radius.
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