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Eventide Prophet

Black Hole Information Paradox Physics

\[T_H = \frac{\hbar c^{3}}{8\pi G M k_B}\]
$21.99 USD
$21.99 USD
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Meet Eventide Prophet. Black holes glow and slowly evaporate. If the glow is purely thermal, what fell in is erased, which quantum mechanics forbids. Recent work suggests the information gets out. How, exactly, is still open. On the mug: T_H = ħc³/(8πGMk_B). Pixel-art full-wrap 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 radiate at T_H = ħc³/(8πGMk_B), about 6×10⁻⁸ K for one solar mass. Whether and how the information that fell in comes back out is an open question.

Eventide Prophet asks the question black holes have kept open for fifty years: where does it go?

In 1974–75 Stephen Hawking showed that quantum effects make a black hole glow with temperature T_H = ħc³/(8πGMk_B), the formula on this mug, and slowly evaporate. Jacob Bekenstein had argued in 1973 that a black hole carries entropy proportional to its horizon area. A worked number: a black hole of one solar mass sits at about 6×10⁻⁸ K, far colder than the 2.7 K cosmic microwave background.

The paradox: if the radiation is exactly thermal, it carries no record of what fell in. When the hole is gone, that information would be erased, which quantum mechanics does not allow. Hawking argued in 1976 that it really is lost. In 1993 Don Page showed that if information is kept, the entropy of the radiation must rise and then fall back to zero, the Page curve. Calculations since 2019 reproduce that curve, suggesting the information gets out. How, exactly, is still open.

Hawking radiation itself has never been observed from a real black hole.

“Everything that falls in,” says the Prophet, “comes out again. I just can't tell you how.”

Equations

\[T_H = \frac{\hbar c^{3}}{8\pi G M k_B}\]
\[T_H \approx 6\times10^{-8}\ \text{K}\times\frac{M_\odot}{M}\]
\[S_{BH} = \frac{k_B c^{3} A}{4 G \hbar}\]
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 \(\mathrm{kg}\)
\(S_{BH}\) Bekenstein–Hawking entropy \(\mathrm{J/K}\)
\(A\) area of the event horizon \(\mathrm{m²}\)

Sources

  1. Hawking (1975) Particle creation by black holes, Commun. Math. Phys. 43, 199
  2. Bekenstein (1973) Black Holes and Entropy, Phys. Rev. D 7, 2333
  3. Hawking (1976) Breakdown of predictability in gravitational collapse, Phys. Rev. D 14, 2460
  4. Page (1993) Information in black hole radiation, PRL 71, 3743
  5. Almheiri, Hartman, Maldacena, Shaghoulian & Tajdini (2021) The entropy of Hawking radiation, Rev. Mod. Phys. 93, 035002

Source Hawking, S. W. (1975). Particle creation by black holes. Communications in Mathematical Physics 43, 199–220.doi.org/10.1007/BF02345020

Field notes

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