Equation 81 · Part 1 · A Horizon Is a Toll Booth, Not a Loophole
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=
What this part means
The expressions on both sides represent the same quantity under the stated assumptions.
Its job in the formula
The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.
Full expression→=→Article meaning
The passage around this formula
which at the horizon itself scales as /(4) — falling as the inverse square of the mass. For a processor of laboratory size =1\, at the horizon of a black hole with the mass measured for the progenitors of the first LIGO gravitational-wave detection, around 30\, , this tidal stress is already about 1.110^5\, , 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 610^{-6}\, across the same centimeter: negligible, and consistent with the…
Learn the underlying idea
An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.
Open the illustrated equality: what the equals sign claims guide →
Sources cited in the surrounding passage
- [16] Observation of Gravitational Waves from a Binary Black Hole Merger ↗
- [14] First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way ↗
These citations provide research context; check each source for the exact claim it supports.