An Application of the General Relativity-type Inversion Formulae: the Derivation of the Fock-Schwinger-Friedmann-Robertson-Walker Christoffel Symbol

Abstract

Similar relationship between Christoffel symbols and Riemann tensors and between gauge potentials and gauge field strengths enable us to treat the Christoffel symbols just like the gauge fields. Restricting the Christoffel symbol by the Fock-Schwinger (FS) condition one obtains the so-call inversion formulae in general relativity theory. These formulae may be utilized for various applications, including the Christoffel symbol-free formulation of the general relativity and calculating the so-called Fock-Schwinger Christoffel symbols for certain Riemann tensors. Here we will derive the Fock-Schwinger-Friedmann-Robertson-Walker (FSFRW) Christoffel symbols.