The Schwarzschild radius, named after the German physicist Karl Schwarzschild, is the radius of the event horizon of a black hole. It defines the boundary beyond which nothing, not even light, can escape the gravitational pull of the black hole. The Schwarzschild radius is given by the formula:
\[ R_s = \frac{2GM}{c^2} \]
where:
- \( R_s \) is the Schwarzschild radius,
- \( G \) is the gravitational constant (\(6.67430 \times 10^{-11} \, \text{m}^3 \text{kg}^{-1} \text{s}^{-2}\)),
- \( M \) is the mass of the object,
- \( c \) is the speed of light in a vacuum (\(2.998 \times 10^8 \, \text{m/s}\)).
### Key Points About the Schwarzschild Radius:
1. **Event Horizon**:
- The Schwarzschild radius represents the radius of the event horizon of a non-rotating black hole. The event horizon is the "point of no return," beyond which the escape velocity exceeds the speed of light.
2. **Proportionality to Mass**:
- The Schwarzschild radius is directly proportional to the mass of the black hole. Doubling the mass of the black hole would double the Schwarzschild radius.
3. **Black Hole Formation**:
- When an object's physical radius becomes smaller than its Schwarzschild radius, it collapses into a black hole. This condition means that the escape velocity at the surface exceeds the speed of light.
4. **Example Calculations**:
- For a black hole with a mass equal to that of the Sun (\( M_{\odot} \approx 1.989 \times 10^{30} \, \text{kg} \)), the Schwarzschild radius is approximately 3 kilometers.
- For Earth, if it were to collapse into a black hole, its Schwarzschild radius would be about 9 millimeters.
5. **Applications**:
- The concept of the Schwarzschild radius is crucial in understanding black holes, their properties, and the regions of space around them. It also plays a significant role in general relativity and astrophysics.
Understanding the Schwarzschild radius helps in comprehending the nature of black holes and the extreme gravitational effects associated with them.
意思是說，來到一個沒有光的所在，來到一個光無法脫逃的所在，
