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f→0f\to0

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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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f→0f\to0

Equation 62 · Evolutionary Physics

A Horizon Is a Toll Booth, Not a Loophole

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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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