← All parts of this equation

Equation 49 · Part 8 · How Fast Can a Horizon Learn Which Path You Took?

fraction

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

What this part means

Divide the expression above the line by the one below it.

Its job in the formula

The expression above the fraction bar is divided by the complete expression below it. The denominator must not be zero.

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.