Equation 66 · Part 3 · A Horizon Is a Toll Booth, Not a Loophole

Symbol r_s^2

GM/r_s^2\approx3.80\times10^{6}\,\mathrm{m\,s^{-2}}

r_s^2

What this part means

$r_s^2$ is squared: multiply the underlying quantity by itself. The square is a mathematical operation, not a second independent variable.

Its job in the formula

$r_s^2$ is squared: multiply the underlying quantity by itself. The square is a mathematical operation, not a second independent variable.

Full expressionSymbol r_s^2Article meaning

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 $\approx$ 4 $\times$ 10^6\, $M_\odot$ , giving a Schwarzschild radius $r_s$ $\approx$ 1.18 $\times$ 10^{10}\, $\mathrm m$ and a horizon-scale acceleration factor GM/ $r_s^2$ $\approx$ 3.80 $\times$ 10^{6}\, $\mathrm{m\,s^{-2}}$ [ 14 ] . At a clearance of just one kilometer above the horizon — a distance smaller than a millionth of the horizon’s own radius — f $\approx$ 8.46 $\times$ 10^{-8} and the required proper acceleration is already a $\approx$ 1.3 $\times$ 10^{10}\, $\mathrm{m\,s^{-2}}$ , more than a billion Earth gravities. Even at a clearance of 1.8 $\times$ 10^6\, $\mathrm{km}$ — about fifteen percent of the horizon’s own…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the surrounding passage

[14] First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way ↗

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