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Integration without integration: new Killing spinor spacetimes

Norbert Van den Bergh UGent (2010) JOURNAL OF PHYSICS CONFERENCE SERIES. 229.
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.
Please use this url to cite or link to this publication:
author
organization
year
type
conference
publication status
published
subject
keyword
Killing spinors, space-times
in
JOURNAL OF PHYSICS CONFERENCE SERIES
J. Phys. Conf. Ser.
editor
R Lazkoz and R Vera
volume
229
issue title
Spanish relativity meeting (ERE 2009)
article_number
012071
pages
4 pages
publisher
IOP
place of publication
Bristol, UK
conference name
Spanish Relativity meeting (ERE 2009)
conference location
Bilbao, Spain
conference start
2009-09-07
conference end
2009-09-11
Web of Science type
Proceedings Paper
Web of Science id
000287182000071
ISSN
1742-6588
DOI
10.1088/1742-6596/229/1/012071
language
English
UGent publication?
yes
classification
P1
copyright statement
I have transferred the copyright for this publication to the publisher
id
1845276
handle
http://hdl.handle.net/1854/LU-1845276
date created
2011-06-29 11:44:29
date last changed
2011-06-29 13:49:35
@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 \ensuremath{\rho} or \ensuremath{\mu}, vanish. Here the general case with non-vanishing \ensuremath{\rho}, \ensuremath{\mu}, \ensuremath{\pi} and \ensuremath{\tau} 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},
  keyword      = {Killing spinors,space-times},
  language     = {eng},
  location     = {Bilbao, Spain},
  pages        = {4},
  publisher    = {IOP},
  title        = {Integration without integration: new Killing spinor spacetimes},
  url          = {http://dx.doi.org/10.1088/1742-6596/229/1/012071},
  volume       = {229},
  year         = {2010},
}

Chicago
Van den Bergh, Norbert. 2010. “Integration Without Integration: New Killing Spinor Spacetimes.” In Journal of Physics Conference Series, ed. R Lazkoz and R Vera. Vol. 229. Bristol, UK: IOP.
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). Presented at the Spanish Relativity meeting (ERE 2009), Bristol, UK: IOP.
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.
MLA
Van den Bergh, Norbert. “Integration Without Integration: New Killing Spinor Spacetimes.” Journal of Physics Conference Series. Ed. R Lazkoz & R Vera. Vol. 229. Bristol, UK: IOP, 2010. Print.