The Edge of a Black Hole
In 1916, while serving on the Russian front during WWI, physicist Karl Schwarzschild found the first exact solution to Einstein's equations of General Relativity. His math showed something terrifying: if you compress any mass into a small enough space, its gravity will become so intense that not even light can escape it.
The boundary around this compressed mass, where the escape velocity exactly equals the speed of light, is called the Event Horizon. The distance from the center of the mass to the Event Horizon is the Schwarzschild Radius ($r_s$).
Every Object Has a Radius
Theoretically, anything can become a black hole if you squeeze it hard enough.
- To make the Earth a black hole, you would have to compress its entire mass into a sphere about the size of a marble ($9 , \text{mm}$).
- To make the Sun a black hole, you would have to compress it into a sphere about $3 , \text{km}$ across.
The Formula
Example Calculation
Calculate the Schwarzschild radius of a massive star $10$ times heavier than our sun ($Mass = 1.989 \times 10^{31} , \text{kg}$).
- Gravitational Constant (G): $6.674 \times 10^{-11}$.
- Speed of Light Squared (c²): $8.987 \times 10^{16}$.
- Numerator: $2 \times (6.674 \times 10^{-11}) \times (1.989 \times 10^{31}) \approx 2.65 \times 10^{21}$.
- Divide by c²: $2.65 \times 10^{21} / 8.987 \times 10^{16} \approx 29,500 , \text{meters}$.
A star that massive would have an event horizon radius of almost $30 , \text{kilometers}$.