The Schwarzschild Radius

We can find the kinetic energy that must be given to a body of massstationary at the surface of a non rotating spherically distributed massand radiusto just remove it into space far away from the body by equating the required kinetic energy to the negative of the gravitational potential energy.

Hence(1)

is called the escape velocity. If the radial velocity of the body is greater than the escape velocity then the body will escape the gravitational influence of the mass.

We know no material particle can travel faster than the speed of lightand might ask 'what happens when the escape velocity reaches the speed of light?' Then v=c and not even light will escape from the surface of the body.

(1) becomeswhich can be rearranged to give the radius that a body of massmust be confined to so that the escape velocity equalsThis value ofis called the Schwarzschild radius and labelled

Every black hole has a radius equal to it's Schwarzschild radius. The actual size of the mass in the black hole may be a great deal smaller than the Schwarzschild radius but we cannot tell, since light cannot pass from inside the black hole to outside. In fact the mass is thought to constitute a singularity at the centre of the hole, where the known laws of physics break down.