Summary: ASTR 1120 Section 1 (3 credit hours): Spring 2006
SUMMARY OF KEY CONCEPTS: WEEK #6
Lecture #11 Reading Chapter 18 (either edition)
We first reviewed the Newtonian concept of a `dark star' or black hole. For any star or planet,
we can calculate the escape velocity the minimum speed an object must have to completely
escape the gravitational influence of the star. This is derived by equating the kinetic energy with
the gravitational potential energy. The escape velocity is large for massive, compact (small
radius) stars. A sufficiently massive, compact star would have an escape velocity larger than the
velocity of light so in Newtonian theory it would be completely dark.
Unfortunately this concept is flawed, since Special Relativity is based on the idea that the speed
of light is a constant for all observers we can't view photons in the same way as tennis balls!
The relativistic theory of black holes dates to Karl Schwarzschild in 1916. He showed that a
spherically symmetric (non-rotating) body of mass M has a critical radius now called the
Schwarzschild radius, given by,
where c is the speed of light and G the gravitational constant. The Schwarzschild radius is very
small for an object of a Solar mass it is 3 km and it scales linearly with mass (so a 10 Solar mass