stationary
at the surface of a non rotating spherically distributed mass
and
radius
to
just remove it into space far away from the body by equating the
required kinetic energy to the negative of the gravitational
potential energy.
A Level Physics Notes: Special and General Relativity – 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
light
and
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) becomes
which
can be rearranged to give the radius that a body of massmust
be confined to so that the escape velocity equals
This
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.
