Linearized general relativity and its quantization

Abstract

We begin by deriving the Einstein equation from the Einstein-Hilbert action integral using variational methods; Variation with respect to the metric and the Palatini variation. The vacuum solution (Schwarzschild solution) is then presented and derived. Weak field approximation is introduced, and the vacuum solution is derived again in this framework.

Higher-order Lagrangians and their effects on the gravitational potential is investigated, but found to not be of particular significance to the quantization procedure that follows.

The quantization of the theory is accomplished through the use of the background field method, and therefore applies for any background space-time.