Equation 79 · Part 8 · A Horizon Is a Toll Booth, Not a Loophole

subscript

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

subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

Full expressionsubscriptArticle meaning

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 $\ell$ falling radially experiences a stretching tidal acceleration between its two ends of approximately $a_{\rm tidal}(r) \approx \frac{2GM}{r^3}\,\ell$ . 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…

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 →

Sources cited in the surrounding passage

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