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Equation 65 · Part 1 · A Horizon Is a Toll Booth, Not a Loophole

Symbol r_s

rs≈1.18×1010 mr_s\approx1.18\times10^{10}\,\mathrm m
rsr_s

What this part means

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

Its job in the formula

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

The passage around this formula

To make this concrete rather than asymptotic, take the mass of Sagittarius A* as measured by the Event Horizon Telescope, M≈\approx4×\times10^6\,M⊙M_\odot , giving a Schwarzschild radius rsr_s≈\approx1.18×\times10^{10}\,m\mathrm m and a horizon-scale acceleration factor GM/rs2r_s^2≈\approx3.80×\times10^{6}\,m s−2\mathrm{m\,s^{-2}} [ 14 ] . At a clearance of just one kilometer above the horizon — a distance smaller than a millionth of the horizon’s own radius — f≈\approx8.46×\times10^{-8} and the required proper acceleration is already a≈\approx1.3×\times10^{10}\,m s−2\mathrm{m\,s^{-2}} , more than a billion Earth gravities. Even at a clearance of 1.8×\times10^6\,km\mathrm{km} — about fifteen percent of the horizon’s own…

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