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Equation 47 · Part 5 · How Fast Can a Horizon Learn Which Path You Took?

=

V(T)=(TT0)−C,V(T)=\left(\frac{T}{T_0}\right)^{-C},
=

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

The nonextremal exponential is not universal. Gralla and Wei find that at zero surface gravity a scalar/Klein–Gordon analogue can cross to power-law overlap, V(T)=(TT0)−CV(T)=\left(\frac{T}{T_0}\right)^{-C}. while in their electromagnetic extremal Kerr limit the relevant horizon flux is expelled: both the surface gravity and electromagnetic decohering flux vanish because the external field does not penetrate the horizon [ 3 ] . For a genuine power law with C>0 , a threshold clock scales as a power of the required overlap rather than a logarithm. For the screened electromagnetic case, no horizon record accumulates through that channel.

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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Sources cited in the surrounding passage

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