Bianchi I metric solutions with nonminimally coupled Einstein-Maxwell gravity theory

Abstract

By using Bianchi I type of homogenous and anisotropic background metric having cylindrical symmetry in x direction of a local cartesian coordinate systems, we solve Einstein Maxwell metric field equations for three different cases. We assume in each case just one component of the four vector potential is non zero. This important condition reaches to some compatible metric solutions. There are obtained several exponentially inflationary expanding metric solutions. This encourages us to investigate their stability nature via dynamical system approach. We obtain unstable source nature in phase space for case A t (t) = 0 while there are stable sink nature in phase space for A x (t) = 0 with A y = A z = 0. For A x (t) = 0 signature of the metric is Lorentzian (−, +, +, +) while for A y = A z = 0 it is Euclidean (−, −, −, −). Furthermore our mathematical calculations show that the anisotropy property plays critical behavior in expansion of the universe.