Examples in (3 + 1 ) GR

Abstract

Important early calculations in (3 + 1 ) cosmological spacetimes were carried out by Audretsch, and Schäfer [1, 2]. Several solutions in a non-cosmological context are [3–10]. In our first example we shall calculate the Fock-Ivanenkocoefficients and the resulting Dirac equations for the Schwarzschild metric (with signature (+ 2 )). The γ matrices are in the standard representation, however because of our signature choice, we have to multiply each of the matrices (B.8), with a factor of + i. Then Eq. (B.9) change sign and Eq. (B.3) holds with ε= + 1.