contains the Kaluza-Klein corrections and acts as a nonlocal source arising from the 5-dimensional Weyl curvature
. Here U is the bulk Weyl scalar, [P.sub.[mu][nu]] is the Weyl stress tensor, [Q.sub.[mu]] is the Weyl energy flux, and [h.sub.[mu][nu]] = [g.sub.[mu][nu]] - [u.sub.[mu]][u.sub.[nu]] denotes the projection tensor orthogonal to the fluid lines.
Other subjects discussed are MachEs principle within general relativity, an algebraic approach to quantum gravity, the abuse of gravity theories in cosmology, PenroseEs Weyl curvature
hypothesis, and twistors, special functions, and the Penrose transform.
For a Riemanian manifold M of dimension m > 3, a straightforward calculation gives that the Weyl curvature
tensor is harmonic if and only if
Our observed Universe would then be devoid of the Weyl curvature
which explains why it is purely described in terms of the Ricci tensor alone.
We may introduce the traceless Weyl curvature tensor W through the decomposition
This shows that, in the presence of metric discontinuity, the field strength f depends on the Weyl curvature alone which is intrinsic to the background space(-time) only when matter and non-null electromagnetic fields are absent.
For this reason we shall review in section 3 the relationship between Bohm's Quantum Potential and the Weyl curvature scalar of the Statistical ensemble of particle-paths (an Abelian fluid) associated to a single particle that was initially developed by .
We shall begin by reviewing the relationship between the Bohm's Quantum Potential and the Weyl curvature scalar of the Statistical ensemble of particle-paths (a fluid) associated to a single particle and that was developed by .