• Black Penrose Diagram physics hoodie, pixel-art Schwarzschild spacetime design, worn by a model, front close-up
  • Black Penrose Diagram physics hoodie, pixel-art Schwarzschild spacetime design, worn by a model, back close-up
  • Black Penrose Diagram physics hoodie, pixel-art Schwarzschild spacetime design, front view
  • Black Penrose Diagram physics hoodie, pixel-art Schwarzschild spacetime design, back view
  • Black Penrose Diagram physics hoodie, pixel-art Schwarzschild spacetime design, turning on a model
  • Black Penrose Diagram physics hoodie, ΨP Pixelated Physics neck label
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Penrose Diagram HoodieALL OF FOREVER, ON ONE PAGE | Pixelated Physics

Penrose Diagram Hoodie – ALL OF FOREVER, ON ONE PAGE | Pixelated Physics

$54.99 USD
$54.99 USD
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Shipping calculated at checkout. Free US shipping · $10 flat shipping outside the US.
Color
Black
Size
S–5XL
Made
To order · shipping times

A Penrose diagram squeezes all of an infinite spacetime onto one page, while keeping light rays at 45°. The maximally extended Schwarzschild black hole, compactified: two exteriors, a horizon cross and a singularity on top. Infinity fits. Pixel-art unisex hoodie in black; equation, symbols and sources in the physics panel below.

Color
Size

Size guideS–5XL · inches

Details

Size & fitS–5XL

Unisex Heavy Blend hoodie (Gildan 18500), classic fit.

SizeWidthLengthSleeve
S202733.5
M222834.5
L242935.5
XL263036.5
2XL283137.5
3XL303238.5
4XL323339.5
5XL343440.5

Measurements in inches. Width and length ±1 in, sleeve (from center back) ±0.75 in.

ShippingFree US

Free US shipping. $10 flat shipping outside the US.

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

A Penrose diagram squeezes all of an infinite spacetime onto one page, while keeping light rays at 45°.

This one is the full Schwarzschild black hole. Start from Kruskal coordinates U and V, in which the horizon is harmless, then take the arctangent of each. Infinity lands on the edges of the diamond.

The right diamond is our universe. The left is a second exterior that the exact solution also contains. The top triangle is the black hole interior, capped by the singularity r = 0, drawn as a zigzag; the bottom one is the time-reversed white hole. The cross through the middle is the horizon.

Once inside, every future-pointing path, at 45° or steeper, hits the zigzag. The lines in the art are surfaces of constant r and constant t.

All of forever, on one page.

Equations

\[ds^2 = -\left(1-\frac{2GM}{c^2r}\right)c^2dt^2 + \frac{dr^2}{1-\frac{2GM}{c^2r}} + r^2d\Omega^2\]
\[u = \arctan U,\qquad v = \arctan V\]
\[UV = \left(1-\frac{r}{2M}\right)e^{r/2M}\quad (G=c=1)\]
SymbolMeaningUnit
\(ds\) spacetime interval \(\mathrm{m}\)
\(t\) Schwarzschild time \(\mathrm{s}\)
\(r\) areal radius \(\mathrm{m}\)
\(M\) black hole mass \(\mathrm{kg}\)
\(d\Omega\) element of solid angle \(\mathrm{sr}\)
\(U, V\) Kruskal–Szekeres null coordinates \(\mathrm{1}\)
\(u, v\) compactified null coordinates \(\mathrm{rad}\)

Sources

  1. Schwarzschild (1916) Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie, Sitzungsber. Preuss. Akad. Wiss., 189
  2. Kruskal (1960) Maximal Extension of Schwarzschild Metric, Phys. Rev. 119, 1743
  3. Penrose (1964) Conformal treatment of infinity, in Relativity, Groups and Topology (Les Houches)
  4. Hawking & Ellis, The Large Scale Structure of Space-Time (1973), Sec. 5.5
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Field notes

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