The Schwarzschild Radius

The boundary around a black hole from inside which nothing can escape is called the event horizon. At the event horizon the escape velocity equals the speed of light, c. Its radius is the Schwarzschild radius, R_s.The escape velocity from the surface of a body of mass M and radius R is v = √(2GM/R). Setting v = c and solving for R gives:R_s ≈ 2GM / c²where G = 6.67 × 10^-11 N m² kg^-2 and c = 3.00 × 10⁸ m s^-1. The Schwarzschild radius is directly proportional to the mass: double the mass, double R_s.Any mass would become a black hole if it were squeezed inside its own Schwarzschild radius. Inside the event horizon the escape velocity is greater than c, so no light or information can get out, which is why black holes cannot be seen directly.Worked example: find the Schwarzschild radius for the mass of the Sun, 1.99 × 10³⁰ kg.
R_s = 2 × 6.67 × 10^-11 × 1.99 × 10³⁰ / (3.00 × 10⁸)²
R_s = 2.65 × 10²⁰ / 9.00 × 10¹⁶ = 2.95 × 10³ m = 2.95 kmThe Sun's actual radius is about 7 × 10⁵ km, so it is nowhere near being a black hole. Because R_s ∝ M, a black hole of 10 solar masses has R_s of about 30 km.