superscript

The passage around this formula

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 $a(r) = \frac{GM/r^2}{\sqrt{f(r)}}$. As r$\to$ $r_s$=2GM/$c^2$ , f$\to$0 and a(r)$\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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