2007
The Sun compressed into a black hole
- Round
- Theory
- Points
- 2
- Level
- Bronze
- Taught in
- Section 10.1
Adapted from IOAA 2007 (Chiang Mai), theory problem 1.14. We have restated it in our own words and kept the original data. The solution was last checked on 22 October 2026.
Suppose the Sun collapsed into a non-rotating black hole, keeping its mass. What would be the radius of its event horizon?
The question gives a mass and asks for the horizon radius, so the needed relation is the Schwarzschild-radius formula.
- For a non-rotating, uncharged black hole, (10.1) gives
- With the constants in that result,
AnswerThe horizon radius would be about 2.95 km. The question is hypothetical. The Sun is not massive enough to end its life as a black hole.
This problem also appears among the olympiad problems of Section 10.1, Black holes and the Schwarzschild radius, which teaches the ideas it uses. Equation and figure numbers refer to the course.