$$30\,M_\odot$$

Equation 82 · Evolutionary Physics

A Horizon Is a Toll Booth, Not a Loophole

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

which at the horizon itself scales as $\ell$ $c^6$/(4$G^2$$M^2$) — falling as the inverse square of the mass. For a processor of laboratory size $\ell$=1\,$\mathrm{cm}$ at the horizon of a black hole with the mass measured for the progenitors of the first LIGO gravitational-wave detection, around 30\,$M_\odot$ , this tidal stress is already about 1.1$\times$10^5\,$\mathrm{m\,s^{-2}}$ , on the order of ten thousand Earth gravities across a single centimeter — enough to disassemble ordinary hardware well before the horizon is reached [ 16 ] . For the Sagittarius A* mass used above, the same formula gives roughly 6$\times$10^{-6}\,$\mathrm{m\,s^{-2}}$ across the same centimeter: negligible, and consistent with the…

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