Eventide Prophet: Black Hole Information Paradox
Relativity & Gravity arc, page 38 of 193. Back to The Pixelated Physics Universe
Who they are
When a black hole evaporates, where does everything that fell in go? Hawking showed in 1974 that black holes radiate, and in 1976 argued that the information inside is lost, which quantum mechanics forbids. Page sharpened the puzzle in 1993. Recent work points toward information escaping, but the question is still open. Eventide Prophet on a pixel-art unisex tee; equation, symbols and sources in the panel below.
Eventide Prophet 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
Hawking showed that black holes glow faintly, with a temperature that goes down as their mass goes up. Bekenstein's entropy is proportional to the horizon area. If evaporation preserves information, the entropy of the radiation has to stay below the black hole's: that is the open information puzzle.
$$ \begin{gathered} T_H = \frac{\hbar c^{3}}{8\pi G M k_B} \\ S_{BH} = \frac{k_B c^{3} A}{4 G \hbar} \\ \begin{gathered} S_{\text{rad}}(t) \le S_{BH}(t) \\ \text{unitary evaporation} \\ (\text{Page 1993}) \end{gathered} \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $T_H$ | Hawking temperature | K |
| $M$ | black-hole mass | kg |
| $k_B$ | Boltzmann constant | J/K |
| $S_{BH}$ | Bekenstein–Hawking entropy | J/K |
| $A$ | horizon area | m² |
| $\hbar, c, G$ | as defined above | J·s, m/s, m³·kg⁻¹·s⁻² |
| $S_{\text{rad}}$ | entanglement entropy of the emitted radiation | J/K |
Status: part of this topic is unsolved, unconfirmed or debated. The text above says which part; treat it as an open question, not settled fact.
Sources
- Bekenstein (1973) Black Holes and Entropy, Phys. Rev. D 7, 2333
- Hawking (1974) Black hole explosions?, Nature 248, 30
- Hawking (1975) Particle creation by black holes, Commun. Math. Phys. 43, 199
- Hawking (1976) Breakdown of predictability in gravitational collapse, Phys. Rev. D 14, 2460
- Encyclopaedia Britannica — Hawking radiation
- Bekenstein (1972) Black holes and the second law, Lett. Nuovo Cimento 4, 737
- Page (1993) Information in black hole radiation, PRL 71, 3743
Crossovers
Eventide Prophet meets Areax (Hawking's Area Theorem). Areax's classical theorem says the horizon area never decreases. Eventide Prophet's black hole evaporates through Hawking radiation and shrinks, which is allowed because quantum effects break the theorem's assumptions. Where the information goes is still open.
Eventide Prophet meets Reversa (Loschmidt's Reversal Paradox). Reversa asks how time-symmetric laws give one-way behaviour. Eventide Prophet asks whether black-hole evaporation loses information, which unitary quantum mechanics forbids. Both puzzles sit where reversibility meets the second law.
Wear the lore
Concept keywords: Black Hole Information Paradox, Eventide Prophet, Relativity & Gravity, physics lore, Pixelated Physics