What is the so-called Schwarzschild-Radius of a Black Hole?
Schwarzschild-Radius or gravitational radius is a characteristic radius associated to every mass object.
In astronomy and astrophysics is defined as the distance (from the center) of a spherical distributed mass to the event horizon of a Schwarzschild black hole. Schwarzschild radius is proportional to the object's mass. (some parameters are here).
Schwarzschild radius was introduced in 1916 when Karl Schwarzschild calculated the exact solution for the gravitational field outside a non-rotating, spherically symmetric star. However it can be derived without the complex mathematical formalism of general relativity, using classical approach.
We are calculated how much mass is needed, that the escaping velocity will be the speed of light
Let's write the kinetic and potential energy: