← All parts of this equation

Equation 49 · Part 11 · How Fast Can a Horizon Learn Which Path You Took?

Denominator: r_0S_0

Eb=GNr03=πr0S0E_b=\frac{G_N}{r_0^3} =\frac{\pi}{r_0S_0}
r0S0r_0S_0

What this part means

The complete quantity below the fraction bar; it must be nonzero for this division.

Its job in the formula

r0r_0S0S_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 ] .…

Read this part in the article →

Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

Open the illustrated fractions: division written vertically guide →

Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.