Integration without integration: new Killing spinor spacetimes
- Author
- Norbert Van den Bergh (UGent)
- Organization
- Abstract
- Non-conformally flat space-times admitting a non-null two-index Killing spinor are investigated by means of the Geroch-Held-Penrose formalism. Claims appearing in the literature that such space-times are all explicitly known are incorrect. This was shown in [5] for the family where, in the canonical frame, the spin coefficients ρ or μ, vanish. Here the general case with non-vanishing ρ, μ, π and τ is re-considered. It is shown that the construction in [4] hinges on the tacit assumption that certain integrability conditions hold, implying two algebraic relations for the spin coefficients and the components of the Ricci spinor. All (conformal classes of) space-times, in which one of these conditions is violated, are obtained by invariant integration. The resulting classes are each others Sachs transform and are characterised by one free function. They admit in general no Killing vectors, but still admit a conformal gauge (different from the trivial unitary gauge) in which a Killing tensor exists.
- Keywords
- Killing spinors, space-times
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-1845276
- MLA
- Van den Bergh, Norbert. “Integration without Integration: New Killing Spinor Spacetimes.” JOURNAL OF PHYSICS CONFERENCE SERIES, edited by R Lazkoz and R Vera, vol. 229, IOP, 2010, doi:10.1088/1742-6596/229/1/012071.
- APA
- Van den Bergh, N. (2010). Integration without integration: new Killing spinor spacetimes. In R. Lazkoz & R. Vera (Eds.), JOURNAL OF PHYSICS CONFERENCE SERIES (Vol. 229). https://doi.org/10.1088/1742-6596/229/1/012071
- Chicago author-date
- Van den Bergh, Norbert. 2010. “Integration without Integration: New Killing Spinor Spacetimes.” In JOURNAL OF PHYSICS CONFERENCE SERIES, edited by R Lazkoz and R Vera. Vol. 229. Bristol, UK: IOP. https://doi.org/10.1088/1742-6596/229/1/012071.
- Chicago author-date (all authors)
- Van den Bergh, Norbert. 2010. “Integration without Integration: New Killing Spinor Spacetimes.” In JOURNAL OF PHYSICS CONFERENCE SERIES, ed by. R Lazkoz and R Vera. Vol. 229. Bristol, UK: IOP. doi:10.1088/1742-6596/229/1/012071.
- Vancouver
- 1.Van den Bergh N. Integration without integration: new Killing spinor spacetimes. In: Lazkoz R, Vera R, editors. JOURNAL OF PHYSICS CONFERENCE SERIES. Bristol, UK: IOP; 2010.
- IEEE
- [1]N. Van den Bergh, “Integration without integration: new Killing spinor spacetimes,” in JOURNAL OF PHYSICS CONFERENCE SERIES, Bilbao, Spain, 2010, vol. 229.
@inproceedings{1845276, abstract = {{Non-conformally flat space-times admitting a non-null two-index Killing spinor are investigated by means of the Geroch-Held-Penrose formalism. Claims appearing in the literature that such space-times are all explicitly known are incorrect. This was shown in [5] for the family where, in the canonical frame, the spin coefficients ρ or μ, vanish. Here the general case with non-vanishing ρ, μ, π and τ is re-considered. It is shown that the construction in [4] hinges on the tacit assumption that certain integrability conditions hold, implying two algebraic relations for the spin coefficients and the components of the Ricci spinor. All (conformal classes of) space-times, in which one of these conditions is violated, are obtained by invariant integration. The resulting classes are each others Sachs transform and are characterised by one free function. They admit in general no Killing vectors, but still admit a conformal gauge (different from the trivial unitary gauge) in which a Killing tensor exists.}}, articleno = {{012071}}, author = {{Van den Bergh, Norbert}}, booktitle = {{JOURNAL OF PHYSICS CONFERENCE SERIES}}, editor = {{Lazkoz, R and Vera, R}}, issn = {{1742-6588}}, keywords = {{Killing spinors,space-times}}, language = {{eng}}, location = {{Bilbao, Spain}}, pages = {{4}}, publisher = {{IOP}}, title = {{Integration without integration: new Killing spinor spacetimes}}, url = {{http://doi.org/10.1088/1742-6596/229/1/012071}}, volume = {{229}}, year = {{2010}}, }
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