Not enough, Rainich also saw that the electromagnetic field tensor is performed from the congruences of two dual surfaces.

Since the electromagnetic field tensor is performed by the main surfaces, it is a curve parameter of the current path like the curvature vector (which is performed by the main normal, and is the geometric expression of both gravitation and accelerated motion), as Rainich already saw.

where the

electromagnetic field tensor can now be expressed by the extended form (given in Section 3)

As in [1], for reasons that will be clear later, we define the

electromagnetic field tensor F via the torsion tensor of spacetime (the anti-symmetric part of the connection [GAMMA]) as follows:

The four-dimensional components of the

electromagnetic field tensor in canonical form are

Meanwhile, the

electromagnetic field tensor is given by

It is a curious fact that the last two relations somehow remind us of the algebraic structure of the components of the

electromagnetic field tensor in physics.

Let us first call the following expression for the covariant components of the

electromagnetic field tensor in terms of the covariant components of the canonical electromagnetic four-potential A:

alpha][beta]] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], constructed from the

electromagnetic field tensor [F.

beta]]) is Maxwell's

electromagnetic field tensor, while [A.

Emulating the way that Maxwell's

electromagnetic field tensor is introduced, we introduce the tensor of a time density field as the rotor of its four-dimensional vector potential

Thus, there is no complete analogy between the physically observable components of the Riemann-Christoffel curvature tensor and Maxwell's

electromagnetic field tensor.