← All parts of this equation

Equation 79 · Part 1 · A Horizon Is a Toll Booth, Not a Loophole

Symbol a_rm tidal

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

What this part means

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.

Its job in the formula

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.

The passage around this formula

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…

Read this part in the article →

Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

See this notation across published equations →

Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.