M. Ziad | Searcharxiv

arXiv2010

Do the Ricci and energy-momentum tensors have "duality'' in the context of their Lie symmetries?

The Ricci and energy-momentum tensors have the same algebraic symmetries. In the Einstein equations they look ``dual'' to each other, in that interchanging them and inverting the gravitational coupling leaves the equations invariant. It may then be expected that their differential symmetry Lie algebras would also be identical. Using cylindrically symmetric static spacetimes it is shown that they are not identical and neither algebra is a subset of the other.

gr-qc↗

arXiv2007

Homotheties of Cylindrically Symmetric Static Manifolds and their Global Extension

Cylindrically symmetric static manifolds are classified according to their homotheties and metrics. In each case the homothety vector fields and the corresponding metrics are obtained explicitly by solving the homothety equations. It turns out that these metrics admit homothety groups $H_m$, where $m=4,5,7,11$. This classification is then used to identify the cylindrically symmetric static spaces admitting the local homotheties, which are globally prohibited due to their topological construction. Einstein's field equations are then used to identify the physical nature of the spaces thus obtained.

gr-qc↗