Black Holes
First image of a black hole — M87*, April 2019, Event Horizon Telescope Collaboration.
A black hole is a region of spacetime where gravity is so extreme that nothing — not particles, not light — can escape once past the event horizon.
Schwarzschild radius
The radius at which escape velocity equals the speed of light:
r_s = 2GM / c²
For the Sun (M = 1.989 × 10³⁰ kg):
r_s = 2 × 6.674e-11 × 1.989e30 / (3e8)²
≈ 2,953 m
≈ 3 km
For Earth: ~9 mm — smaller than a marble.
Notable black holes
| Name | Type | Mass (M☉) | Distance |
|---|---|---|---|
| Sgr A* | Supermassive | 4.1 × 10⁶ | 26,000 ly |
| M87* | Supermassive | 6.5 × 10⁹ | 53.5 Mly |
| Cygnus X-1 | Stellar | ~21 | 6,100 ly |
| GW150914 | Binary merger | 62 | 1.3 Bly |
| TON 618 | Ultramassive | 6.6 × 10¹⁰ | 10.4 Bly |
Hawking radiation
In 1974, Stephen Hawking showed that black holes are not completely black — they emit thermal radiation due to quantum effects near the horizon. The temperature of a black hole is:
T_H = ℏc³ / (8πGMk_B)
For a solar-mass black hole, T_H ≈ 60 nanokelvin — far colder than the CMB (2.7 K). It would take approximately 2 × 10⁶⁷ years to evaporate completely via Hawking radiation.
Information paradox
If a black hole evaporates completely, what happens to the information about everything that fell in? Hawking’s original claim (1976) was that it was destroyed — violating quantum unitarity. The debate is unresolved. Current leading candidates:
- Holographic principle — information is encoded on the horizon surface
- Island formula — Page curve recovered via replica wormholes (2019)
- Firewall — information preserved but at the cost of a horizon that burns infalling observers
The answer almost certainly requires a theory of quantum gravity we don’t have yet.