Homotheties of Cylindrically Symmetric Static Manifolds and their Global Extension

Details Homotheties of Cylindrically Symmetric Static Manifolds and their Global Extension Homotheties of Cylindrically Symmetric Static Manifolds and their Global Extension

2007-02-06

arxiv.org/abs/gr-qc/0702034v1

Class. Quantum Grav. 17(2000)345-349

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

8 pages, no figure

Scientific paper

10.1088/0264-9381/17/2/305

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.

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