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 the surface would equal the speed of light. It marks the boundary of a black hole, beyond which nothing can escape.

5 Must Know Facts For Your Next Test

1. The Schwarzschild radius is given by $R_s = \frac{2GM}{c^2}$, where $G$ is the gravitational constant, $M$ is the mass of the object, and $c$ is the speed of light.
2. Any object smaller than its Schwarzschild radius becomes a black hole.
3. The concept was derived from Karl Schwarzschild's solution to Einstein's field equations in general relativity.
4. For a black hole with a mass equal to that of our Sun, the Schwarzschild radius is approximately 3 kilometers.
5. The event horizon of a non-rotating black hole corresponds to its Schwarzschild radius.

Review Questions

• What happens when an object's size is reduced below its Schwarzschild radius?
• How is the Schwarzschild radius related to escape velocity and the speed of light?
• Who provided the solution leading to the concept of Schwarzschild radius in general relativity?

Related terms

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

General Relativity: Einstein's theory describing gravity as a curvature of spacetime caused by mass and energy.

Escape Velocity: $v_{esc} = \sqrt{\frac{2GM}{r}}$, it is the minimum velocity needed for an object to break free from another object's gravitational pull.