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Equation 49 · Part 6 · How Fast Can a Horizon Learn Which Path You Took?

Symbol S_0

Eb=GNr03=πr0S0E_b=\frac{G_N}{r_0^3} =\frac{\pi}{r_0S_0}
S0S_0

What this part means

S0S_0 occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

Its job in the formula

S0S_0 occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

The passage around this formula

The sharper 2026 challenge comes from quantum rather than semiclassical extremality. Biggs and Trezzi study near-extremal charged Reissner–Nordström black holes with quantum fluctuations of the near-horizon geometry. In their electromagnetic single-charge-superposition setup, a spin-induced gap in the black-hole spectrum makes the late-time decoherence rate vanish when the energy above extremality lies below Eb=GNr03=πr0S0E_b=\frac{G_N}{r_0^3} =\frac{\pi}{r_0S_0}. in their natural-unit conventions. They establish the zero through quartic order in the interaction and conjecture it to all orders for the stated opposite-dipole geometry; above the gap, the quantum-corrected rate remains below the semiclassical prediction [ 8 ] .…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the surrounding passage

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