Cylindrically and toroidally symmetric solutions with a cosmological constant

Details Cylindrically and toroidally symmetric solutions with a cosmological constant Cylindrically and toroidally symmetric solutions with a cosmological constant

2010-11-26

arxiv.org/abs/1011.5826v1

J.Phys.Conf.Ser.314:012100,2011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

4 pages, 2 figures. To appear in the Proceedings of The Spanish Relativity Meeting (ERE2010), Journal of Physics: Conference S

Scientific paper

10.1088/1742-6596/314/1/012100

Cylindrical-like coordinates for constant-curvature 3-spaces are introduced and discussed. This helps to clarify the geometrical properties, the coordinate ranges and the meaning of free parameters in the static vacuum solution of Linet and Tian. In particular, when the cosmological constant is positive, the spacetimes have toroidal symmetry. One of the two curvature singularities can be removed by matching the Linet-Tian vacuum solution across a toroidal surface to a corresponding region of the dust-filled Einstein static universe. Some other properties and limiting cases of these space-times are also described, together with their generalisation to higher dimensions.

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