%0 Journal Article %1 Emparan2002Generalized %A Emparan, Roberto %A Reall, Harvey S. %D 2002 %K 5d-bhs, blackring %T Generalized Weyl Solutions %U http://arxiv.org/abs/hep-th/0110258 %X It was shown by Weyl that the general static axisymmetric solution of the vacuum Einstein equations in four dimensions is given in terms of a single axisymmetric solution of the Laplace equation in three-dimensional flat space. Weyl's construction is generalized here to arbitrary dimension \$D4\$. The general solution of the D-dimensional vacuum Einstein equations that admits D-2 orthogonal commuting non-null Killing vector fields is given either in terms of D-3 independent axisymmetric solutions of Laplace's equation in three-dimensional flat space or by D-4 independent solutions of Laplace's equation in two-dimensional flat space. Explicit examples of new solutions are given. These include a five-dimensional asymptotically flat ``black ring'' with an event horizon of topology S^1 x S^2 held in equilibrium by a conical singularity in the form of a disc.

@article{Emparan2002Generalized, abstract = {{It was shown by Weyl that the general static axisymmetric solution of the vacuum Einstein equations in four dimensions is given in terms of a single axisymmetric solution of the Laplace equation in three-dimensional flat space. Weyl's construction is generalized here to arbitrary dimension \$D\ge 4\$. The general solution of the D-dimensional vacuum Einstein equations that admits D-2 orthogonal commuting non-null Killing vector fields is given either in terms of D-3 independent axisymmetric solutions of Laplace's equation in three-dimensional flat space or by D-4 independent solutions of Laplace's equation in two-dimensional flat space. Explicit examples of new solutions are given. These include a five-dimensional asymptotically flat ``black ring'' with an event horizon of topology S^1 x S^2 held in equilibrium by a conical singularity in the form of a disc.}}, added-at = {2019-02-26T10:37:35.000+0100}, archiveprefix = {arXiv}, author = {Emparan, Roberto and Reall, Harvey S.}, biburl = {https://www.bibsonomy.org/bibtex/287d6e1f75bb34098e96f2844b5905623/acastro}, citeulike-article-id = {7529470}, citeulike-linkout-0 = {http://arxiv.org/abs/hep-th/0110258}, citeulike-linkout-1 = {http://arxiv.org/pdf/hep-th/0110258}, day = 17, eprint = {hep-th/0110258}, interhash = {9273979fdc03ca699143390ff07525c8}, intrahash = {87d6e1f75bb34098e96f2844b5905623}, keywords = {5d-bhs, blackring}, month = feb, posted-at = {2010-07-21 17:11:03}, priority = {2}, timestamp = {2019-02-26T10:37:35.000+0100}, title = {{Generalized Weyl Solutions}}, url = {http://arxiv.org/abs/hep-th/0110258}, year = 2002 }