Schwarzschild

Definition

The Schwarzschild solution is an exact solution to Einstein's field equations in general relativity that describes the gravitational field outside a spherical mass. It is characterized by the Schwarzschild radius, beyond which nothing can escape the gravitational pull.

5 Must Know Facts For Your Next Test

1. The Schwarzschild radius defines the event horizon of a black hole.
2. It assumes a non-rotating, spherically symmetric mass without electric charge.
3. The Schwarzschild metric is given by $ds^2 = -(1 - \frac{2GM}{c^2r})c^2dt^2 + (1 - \frac{2GM}{c^2r})^{-1}dr^2 + r^2d\Omega^2$.
4. For objects with mass greater than three times that of the Sun, the Schwarzschild radius becomes significant enough to form a black hole.
5. At distances much greater than the Schwarzschild radius, the metric approximates Newtonian gravity.

Review Questions

• What physical boundary does the Schwarzschild radius define?
• In what scenarios is the Schwarzschild solution applicable?
• How does the Schwarzschild metric modify our understanding of space and time near massive objects?

Related terms

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

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

Gravitational Singularity: A point in space where gravitational forces cause matter to have infinite density and zero volume.