Gravity III — First Applications

Abstract

After the development of the theory, it is now time to look at some applications. Historically the first solution to Einstein’s field equations was found by Schwarzschild, in 1916, who considered the fields of a mass-point and a spherically-symmetric star. Here we start with the vacuum part of this problem, and its extension to black holes. We will do this by fairly elementary techniques, keeping the entries in the ${\bar h}$-function to the fore, and thereby foregoing manifest gauge covariance. In the next lecture you will see how the derivations can be improved considerably, by what we call the ‘intrinsic method’, in which explicit position-gauge covariance is maintained throughout.