Schwarzschild radius

Definition

The Schwarzschild radius is the radius of a sphere such that, if all the mass of an object were to be compressed within that sphere, the escape velocity from its surface would equal the speed of light. It is a key concept in understanding black holes.

5 Must Know Facts For Your Next Test

1. The Schwarzschild radius is given by the formula $R_s = \frac{2GM}{c^2}$, where $G$ is the gravitational constant, $M$ is the mass of the object, and $c$ is the speed of light.
2. It defines the event horizon of a black hole, beyond which nothing can escape.
3. For Earth, the Schwarzschild radius is approximately 9 millimeters.
4. The concept was derived from Karl Schwarzschild's solution to Einstein's field equations in general relativity.
5. It implies that any object with a physical radius smaller than its Schwarzschild radius will form a black hole.

Review Questions

• What happens to an object when it collapses within its Schwarzschild radius?
• Derive the formula for calculating the Schwarzschild radius.
• Why is the Schwarzschild radius significant in understanding black holes?

Related terms

Event Horizon: A boundary surrounding a black hole beyond which no information or matter can escape.

Escape Velocity: The minimum speed needed for an object to break free from another object's gravitational attraction without further propulsion.

General Relativity: Einstein's theory describing gravity as a property of space and time, or spacetime, which curves around masses.