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Equation 82 · Part 1 · A Horizon Is a Toll Booth, Not a Loophole

Symbol M_odot

30 M⊙30\,M_\odot
M⊙M_\odot

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MoM_odot 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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which at the horizon itself scales as ℓ\ell c6c^6/(4G2G^2M2M^2) — falling as the inverse square of the mass. For a processor of laboratory size ℓ\ell=1\,cm\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⊙M_\odot , this tidal stress is already about 1.1×\times10^5\,m s−2\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×\times10^{-6}\,m s−2\mathrm{m\,s^{-2}} across the same centimeter: negligible, and consistent with the…

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