Part III
General Relativity
We have now studied enough vector and tensor analysis that we may apply the
mathematics to physics. We begin by looking at the familiar classical gravitational
force from a new perspective, as a geometric effect. To develop this idea fully, we
return briefly to mathematics and study curvature in a Riemann space, from which
the general relativistic field equations of gravity follow in a natural way.
As the most fundamental application of the field equations, we then study the
spherically symmetric gravitational field solution of Schwarzschild, which describes
the solar system quite well. This is the oldest and most important exact solution in the
theory. It provides a description of the solar system that has been tested to impressive
accuracy.
Then we progress to much stronger gravitational fields, such as those of a neutron
star or a black hole, that is a collapsed star. To study the collapse of matter to a black
hole we consider the classic example of a dust ball with negligible pressure.
Next we consider black holes themselves and some of their extraordinary properties. One of the most interesting properties that we study is their emission of radiation
like a black body, the Hawking radiation.
Finally we consider weak gravitational fields, for which the theory becomes linear.
As an important application we study gravitational waves; these have been detected
and a new window on the universe has thereby been opened. In particular the waves
from the merger of black holes and neutron stars have been detected so the fields
of gravitational wave physics, black hole physics and neutron star physics have
expanded and become closely connected.