Abstract

We address the nature of torque and the Coriolis forces as dynamic properties of the spacetime metric and the stress-energy tensor. The inclusion of torque and Coriolis effects in Einstein's field equations may lead to significant advancements in describing novae and supernovae structures, galactic formations, their center supermassive black holes, polar jets, accretion disks, spiral arms, galactic halo formations and advancements in unification theory as demonstrated in section five. We formulate these additional torque and Coriolis forces terms to amend Einstein's field equations and solve for a modified Kerr-Newman metric. Lorentz invariance conditions are reconciled by utilizing a modified metrical space, which is not the usual Minkowski space, but the U₄ space. This space is a consequence of the Coriolis force acting as a secondary effect generated from the torque terms. The equivalence principle is preserved using an unsymmetric affine connection. Further, the U₁ Weyl gauge is associated with the electromagnetic field, where the U₄ space is four copies of U₁. Thus, the form of metric generates the dual torus as two copies of U₁ x U₁, which we demonstrate through the S³ spherical space, is related to the SU₂ group and other Lie groups. Hence, the S⁴ octahedral group and the cuboctahedron group of the GUT (Grand Unification Theory) may be related to our U₄ space in which we formulate solutions to Einstein's field equations with the inclusion of torque and Coriolis forces.