Spacetime curvature general relativity

In elementary differential geometry, therefore, the electromagnetic helix produces a nonzero T, and tangent vectors are characteristic of curved spacetime in general relativity. The scalar curvature in elementary differential geometry is... 

To consider magnetic flux density components of IAIV, Q must have the units of weber and R, the scalar curvature, must have units of inverse square meters. In the flat spacetime limit, R 0, so it is clear that the non-Abelian part of the field tensor, Eq. (6), vanishes in special relativity. The complete field tensor F vanishes [1] in flat spacetime because the curvature tensor vanishes. These considerations refute the Maxwell-Heaviside theory, which is developed in flat spacetime, and show that 0(3) electrodynamics is a theory of conformally curved spacetime. Most generally, the Sachs theory is a closed field theory that, in principle, unifies all four fields gravitational, electromagnetic, weak, and strong. 

In Sachs great generalization of a combined general relativity and electrodynamics, we are also speaking of spacetime curvature functions, and a unified field theory. See also Sachs chapter on symmetry in electrodynamics from special to general relativity, macro to quantum domains in this series of volumes on modern nonlinear optics (Part 1, 11th chapter). 

We note that Sachs epochal unification of general relativity and electrodynamics [27] does cover the quarks and gluons causally, as well as fermions and bosons. We point out that curvature of spacetime involves both positive and negative curvatures—with time involved as well as space. Certainly the theory is compatible with the consideration of time as a special form of EM energy. 

In general relativity, the metric tensor is determined by the curvature of spacetime and the interval generalizes to... 

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