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Equation 61 · Part 5 · A Horizon Is a Toll Booth, Not a Loophole

Symbol c^2

r→rs=2GM/c2r\to r_s=2GM/c^2
c2c^2

What this part means

The square of c: multiply c by itself.

Its job in the formula

c2c^2 is an input to the expression that computes the quantity on the left.

The passage around this formula

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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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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Sources cited in the article section

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