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Published equation contexts

atidal(r)≈2GMr3 ℓa_{\rm tidal}(r) \approx \frac{2GM}{r^3}\,\ell

Why this formula appears here

The bill here is tidal, not electromagnetic or mechanical, and it is the one place this construction is bounded directly by what has actually been observed rather than by an idealization. A rigid processor of size ℓ\ell falling radially experiences a stretching tidal acceleration between its two ends of approximately atidal(r)≈2GMr3 ℓa_{\rm tidal}(r) \approx \frac{2GM}{r^3}\,\ell. 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…

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atidala_{\rm tidal}

Symbol a_rm tidal

ara_rm tidal 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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rr

Symbol r

r occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

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r3r^3

Symbol r^3

r3r^3 occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

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How to interpret it

With a fixed numerator, increasing a nonzero denominator reduces the fraction. Its accuracy depends on the assumptions and range of use described in the article.

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Published contexts (1)

A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.

atidal(r)≈2GMr3 ℓ,a_{\rm tidal}(r) \approx \frac{2GM}{r^3}\,\ell,

Equation 79 · Evolutionary Physics

A Horizon Is a Toll Booth, Not a Loophole

This equation gives an approximation: it relates the quantities while allowing an approximation.

The bill here is tidal, not electromagnetic or mechanical, and it is the one place this construction is bounded directly by what has actually been observed rather than by an idealization. A rigid processor of size ℓ\ell falling radially experiences a stretching tidal acceleration between its two ends of approximately atidal(r)≈2GMr3 ℓa_{\rm tidal}(r) \approx \frac{2GM}{r^3}\,\ell. 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…

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