• Pixel-art sticker of Horizia, personifying Schwarzschild Radius, with the caption “Check In, Never Out.”

IndexRelativity & CosmosSticker

Horizia

Schwarzschild Radius Physics

\[r_s = \frac{2GM}{c^2}\]
Regular price $4.99 USD
Regular price Sale price $4.99 USD
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Meet Horizia, where you check in but never out: squeeze a mass inside its Schwarzschild radius, rs = 2GM/c², and nothing, not even light, can get back out from inside that horizon. For the Sun's mass, rs is about 2.95 km. Pixel-art kiss-cut sticker in 2, 3, 4 and 6 inches; equation, symbols and sources in the physics panel below.

Size
Surface

Flat $6 shipping worldwideMade to order, ships in 2–5 business days

Details

Size3″ × 3″

3″ × 3″ kiss-cut sticker.

Shipping

Flat $6 shipping on every order, worldwide, whatever's in it.

Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

Meet Horizia, a horizon: squeeze any mass inside her radius and not even light gets back out.

In 1916, months after Einstein published general relativity, Karl Schwarzschild found its exact solution for the spacetime around a spherical mass. It contains a special radius, r_s = 2GM/c². If all the mass lies inside that radius, it forms a black hole, and r_s marks the event horizon: from inside it, every path, even for light, leads inward.

The radius scales directly with mass. For the Sun's mass, r_s is about 2.95 kilometres; for Earth's, about 9 millimetres. Neither is a black hole, because their mass is spread far wider than that.

Astronomers have found black holes from a few to tens of solar masses, and supermassive ones in galaxy centres. The Event Horizon Telescope imaged the shadow of the black hole in galaxy M87 in 2019 and of Sagittarius A* at the centre of the Milky Way in 2022.

The Schwarzschild solution is for a non-rotating, uncharged mass. Real black holes spin, which changes the horizon's size. What happens at the centre is an open question for a quantum theory of gravity.

Equations

\[r_s = \frac{2GM}{c^2}\]
Symbols
SymbolMeaningUnit
\(r_s\) Schwarzschild radius \(\mathrm{m}\)
\(G\) Newtonian constant of gravitation \(\mathrm{N·m²/kg²}\)
\(M\) mass \(\mathrm{kg}\)
\(c\) speed of light in vacuum \(\mathrm{m/s}\)