Cylindrically and toroidally symmetric solutions with a cosmological constant

Article

Cylindrically and toroidally symmetric solutions with a cosmological constant

Podolský, J.; Griffiths, J.

J. Phys. Conf. Ser. 314, 012100 (2011)

Abstract

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.

Institute authors

Podolský, Jiří

Supported by

GACR 202/08/0187 — Exact solutions in higher dimensional and classical gravity
GACR 202/09/0772 — Current problems of gravitation, general relativity and relativistic astrophysics
LC06014 — Centrum teoretické astrofyziky

BibTeX

@article{UTF434,
  author        = {Podolský, J. and Griffiths, J.},
  title         = {{Cylindrically and toroidally symmetric solutions with a cosmological constant}},
  journal       = {J. Phys. Conf. Ser.},
  volume        = {314},
  pages         = {012100},
  year          = {2011},
  eprint        = {1011.5826},
  archivePrefix = {arXiv},
}