Spatiotemporal jumps as particular solutions in geodesic trajectories with the Gödel metric on an extended manifold

Abstract

Using the Gödel metric, we obtain some relevant solutions compatible with spatiotemporal jumps for the geodesic equations, by using an extension of General Relativity with nonzero boundary terms, which are described on an extended manifold generated by the connections delta Gamma ^{mu }_{alpha beta } = b,U^{mu },g_{alpha beta }. These terms are given by a flow of velocities with components U^{nu }: 3,b^2,nabla _{nu }U^{nu }=g^{alpha beta }, delta R_{alpha beta } = lambda left[ sleft( x^{alpha }right) right] ,g^{alpha beta }, delta g_{alpha beta } in the varied Einstein–Hilbert action. The solutions are valid for an arbitrary equation of state with ordinary matter: Omega =P/(c^2,rho ) = frac{left( frac{omega }{c}right) ^2-lambda (s)}{left( frac{omega }{c}right) ^{2}+lambda (s)}.