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Hawkara

Hawking Radiation Physics

\[T_H = \frac{\hbar c^{3}}{8\pi G M k_B}\]
$21.99 USD
$21.99 USD
할인 품절
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Can a black hole shine? Hawkara thinks so. In 1974 Stephen Hawking predicted that quantum effects make black holes glow with temperature TH = ħc³/(8πGMkB). Smaller holes are hotter and slowly evaporate. For star-sized black holes it is far too faint to see, so it remains unobserved. Pixel-art black ceramic mug in 11 or 15 oz; equation, symbols and sources in the physics panel below.

Shipping calculated at checkout by destinationMade to order, ships in ~10 days

Details

Size & material11oz · 15oz

Black glossy ceramic mug with a C-handle. Lead- and BPA-free.

  • 11oz: 0.33 l
  • 15oz: 0.44 l
CareDishwasher & microwave safe

Dishwasher safe (top rack) or hand wash. Microwave safe.

ShippingBy destination

Shipping calculated at checkout by destination.

Made to order: about 10 days of production and handling before it ships.

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

Black holes emit thermal radiation with a temperature inversely proportional to their mass. For a black hole with the mass of the Sun that temperature is only about 60 billionths of a kelvin, far colder than the cosmic background.

Hawkara is a black hole, and even she leaks, in theory.

In 1974 Stephen Hawking applied quantum theory to the region just outside a black hole's horizon and found that the hole should glow like a warm body, with the temperature on this mug. Nothing crosses back out of the horizon; the radiation arises from the quantum fields just outside it.

The temperature goes down as the mass goes up. A black hole with the mass of the Sun would sit at about sixty billionths of a kelvin, far colder than the cosmic microwave background, the faint blackbody glow left over from the early universe, so today it absorbs more than it emits. Small black holes would be hot, lose mass, get hotter, and eventually evaporate.

EVEN I LEAK. is a prediction, not an observation. Hawking radiation from a real black hole has never been seen; it is far too faint. Laboratory analogues, such as sound waves in a flowing ultracold gas, have shown closely related effects.

Hawkara keeps almost everything. Almost.

Equations

\[T_H = \frac{\hbar c^{3}}{8\pi G M k_B}\]
\[T_H \approx 6\times10^{-8}\ \text{K}\times\frac{M_\odot}{M}\]
SymbolMeaningUnit
\(T_H\) Hawking temperature of a black hole \(\mathrm{K}\)
\(\hbar\) reduced Planck constant \(\mathrm{J·s}\)
\(c\) speed of light in vacuum \(\mathrm{m/s}\)
\(G\) Newtonian constant of gravitation \(\mathrm{m³·kg⁻¹·s⁻²}\)
\(M\) black hole mass \(\mathrm{kg}\)
\(k_B\) Boltzmann constant \(\mathrm{J/K}\)
\(M_\odot\) mass of the Sun \(\mathrm{kg}\)

Sources

  1. Hawking (1974) Black hole explosions?, Nature 248, 30
  2. Hawking (1975) Particle creation by black holes, Commun. Math. Phys. 43, 199
  3. Encyclopaedia Britannica — Hawking radiation
  4. Steinhauer (2016) Observation of quantum Hawking radiation and its entanglement in an analogue black hole, Nat. Phys. 12, 959
  5. NobelPrize.org — The Nobel Prize in Physics 2006 (Mather and Smoot, blackbody form of the cosmic microwave background)

Source Hawking, S. W. (1974). Black hole explosions? Nature 248, 30–31.doi.org/10.1038/248030a0

Field notes

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