Spaghetta: Black Hole Physics / Spaghettification Stretch

Relativity & Gravity arc, page 35 of 193. Back to The Pixelated Physics Universe

Who they are

A black hole doesn’t just pull you in. It pulls your feet harder than your head. Tidal stretch grows as one over distance cubed. At the horizon of a 10-solar-mass black hole it is about twenty million times Earth’s gravity; at the Milky Way’s four-million-solar-mass black hole it is far gentler, and you would cross unharmed. Spaghetta on a pixel-art unisex tee; equation, symbols and sources in the panel below.

Spaghetta is a character of the Relativity & Gravity arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.

The physics

Gravity pulls harder on the near side of a body than on the far side, and that difference grows as one over r cubed. Near a small black hole the difference becomes large enough to stretch an infalling object into a long thin strand.

$$ \begin{gathered} \Delta a \approx \frac{2GM\,L}{r^{3}} \\ r_s = \frac{2GM}{c^{2}} \end{gathered} $$

Symbol Meaning SI unit
$\Delta a$ difference in gravitational acceleration across the body m/s²
$M$ black-hole mass kg
$L$ length of the body along the radial direction m
$r$ distance from the centre m
$r_s$ Schwarzschild radius m

Sources

Crossovers

Spaghetta meets The Limit Keeper (Chandrasekhar Limit). The Limit Keeper says how heavy a white dwarf can get. Spaghetta adds that the tidal stretch near a compact object grows as one over distance cubed. Near a small black hole it can pull a body apart before it crosses the horizon.

Spaghetta meets Areax (Hawking's Area Theorem). Spaghetta tears infalling matter apart. Areax only cares about what happens to the horizon: in classical general relativity it never shrinks, so everything Spaghetta feeds in adds to the area.

Wear the lore

Concept keywords: Black Hole Physics / Spaghettification Stretch, Spaghetta, Relativity & Gravity, physics lore, Pixelated Physics