11. Dark Stars and Black Holes

Definitions

Dark Star

• A dark star is an object by which it's escape velocity exceeds that of the speed of light

Schwarzschild Radius

• Radius beyond which light cannot escape

Event Horizon

• The point at which nothing can escape

Derivations

Taking our equation for escape velocity

$$v = \sqrt{\dfrac{2GM}{R}}$$

subbing in the speed of light $c$ for $v$

$$R_s = \dfrac{2GM}{c^2}$$

this is the Schwarzschild Radius for an object of mass $M$