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Published equation contexts

a(r)=GM/r2f(r)a(r) = \frac{GM/r^2}{\sqrt{f(r)}}

Why this formula appears here

Staying in place first. A static observer at radius r in Schwarzschild spacetime is not in free fall and must be continuously supported against the horizon’s pull, at proper acceleration a(r)=GM/r2f(r)a(r) = \frac{GM/r^2}{\sqrt{f(r)}}. As r→\to rsr_s=2GM/c2c^2 , f→\to0 and a(r)→\to∞\infty : holding station arbitrarily close to a horizon costs arbitrarily large continuous thrust, sourced from arbitrarily large continuous energy expenditure, which is exactly the situation Unruh’s original analysis and the long literature it produced treat as the flip side of a diverging local temperature for an accelerated or static near-horizon observer [ 9 , 12 ] .

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ff

Symbol f

f occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

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f(r)\sqrt{f(r)}

Denominator: sqrtf(r)

The complete quantity below the fraction bar; it must be nonzero for this division.

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With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.

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Published contexts (1)

A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.

a(r)=GM/r2f(r).a(r) = \frac{GM/r^2}{\sqrt{f(r)}}.

Equation 60 · 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 in place first. A static observer at radius r in Schwarzschild spacetime is not in free fall and must be continuously supported against the horizon’s pull, at proper acceleration a(r)=GM/r2f(r)a(r) = \frac{GM/r^2}{\sqrt{f(r)}}. As r→\to rsr_s=2GM/c2c^2 , f→\to0 and a(r)→\to∞\infty : holding station arbitrarily close to a horizon costs arbitrarily large continuous thrust, sourced from arbitrarily large continuous energy expenditure, which is exactly the situation Unruh’s original analysis and the long literature it produced treat as the flip side of a diverging local temperature for an accelerated or static near-horizon observer [ 9 , 12 ] .

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