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t∗∼(β/2π)ln⁡St_* \sim (\beta/2\pi)\ln S

Why this formula appears here

One honest caveat belongs here rather than in a footnote. The estimate t∗t_* ∼\sim (β\beta/2π\pi)ln⁡\ln S treats emission as though every mode escaped with equal ease, when a real Schwarzschild hole’s greybody factors suppress low-angular-momentum, long-wavelength quanta relative to a naive blackbody count. That suppression changes the effective rate at which new, usable radiation becomes available by an order-one-to-few numerical factor; it does not change the logarithmic scaling in S that makes t∗t_* so much shorter than the hole’s own light-crossing or evaporation timescales, and it is exactly the kind of correction the fast-scrambling conjecture was framed to survive [ 2 ] . The millisecond figure…

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t∗t_*

Symbol t_*

t∗t_* is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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β\beta

Symbol β

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π\pi

Symbol pi

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SS

Symbol S

S is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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t∗∼(β/2π)ln⁡St_* \sim (\beta/2\pi)\ln S

Equation 93 · Evolutionary Physics

The Bit Comes Back Before the Bearing

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

One honest caveat belongs here rather than in a footnote. The estimate t∗t_* ∼\sim (β\beta/2π\pi)ln⁡\ln S treats emission as though every mode escaped with equal ease, when a real Schwarzschild hole’s greybody factors suppress low-angular-momentum, long-wavelength quanta relative to a naive blackbody count. That suppression changes the effective rate at which new, usable radiation becomes available by an order-one-to-few numerical factor; it does not change the logarithmic scaling in S that makes t∗t_* so much shorter than the hole’s own light-crossing or evaporation timescales, and it is exactly the kind of correction the fast-scrambling conjecture was framed to survive [ 2 ] . The millisecond figure…

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