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New Geometry with All Killing Vectors Spanning the Poincaré Algebra |
| HUANG Chao-Guang1,2**,TIAN Yu3,WU Xiao-Ning4,5,XU Zhan6,ZHOU Bin7 |
1Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049
2Theoretical Physics Center for Science Facilities, Chinese Academy of Sciences, Beijing 100049
3Graduate University of Chinese Academy of Sciences, Beijing 100049
4Institute of Mathematics, Academy of Mathematics and System Science, Chinese Academy of Sciences, Beijing 100190
5Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing 100190
6Department of Physics, Tsinghua University, Beijing 100084
7Department of Physics, Beijing Normal University, Beijing 100875 |
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| Cite this article: |
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HUANG Chao-Guang, TIAN Yu, WU Xiao-Ning et al 2012 Chin. Phys. Lett. 29 040303 |
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Abstract The new four-dimensional geometry whose Killing vectors span the Poincaré algebra is presented and its structure is analyzed. The new geometry can be regarded as the Poincaré-invariant solution of the degenerate extension of the vacuum Einstein field equations with a negative cosmological constant and provides a static cosmological spacetime with a Lobachevsky space. The motion of free particles in the spacetime is discussed.
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Received: 14 September 2011
Published: 04 April 2012
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| PACS: |
03.30.+p
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(Special relativity)
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04.20.Cv
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(Fundamental problems and general formalism)
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02.20.Sv
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(Lie algebras of Lie groups)
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02.90.+p
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(Other topics in mathematical methods in physics)
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| [1] Bacry H and Lévy-Leblond J M 1968 J. Math. Phys. 9 1605[2] Guo H Y, Wu H T and Zhou B 2009 Phys. Lett. B 670 437[3] Guo H Y, Huang C G, Wu H T and Zhou B 2010 Sci. Chin.–Phys. Mech. Astron. 53 591[4] The transformations are the subset of the general fractional linear transformations by Umow N A 1910 Physik Zeit 11 905Weyl H 1923 Mathemathische Analyse des Raumproblems (Berlin: Springer)Fock V 1964 The Theory of Spacetime and Gravitation (Orxford: Pergamon Press) and references thereinHua L K 1982 Starting with Unit Circle, a Lecture Note (New York: Springer-Verlag).[5] Aldrovandi R and Pereira J G 1998 A Second Poincaré Group arXiv:gr-qc/9809061[6] Aldrovandi R, Barbosa A L, Calçada M and Pereira J G 2003 Found. Phys. 33 613[7] Huang C G, Tian Y, Wu X N, Xu Z and Zhou B 2012 Commun. Theor. Phys. 57 553 (in press)[8] Ashtekar A 1986 Phys. Rev. Lett. 57 2244Ashtekar A 1987 Phys. Rev. D 36 1587[9] Jacobson T and Smolin L 1988 Nucl. Phys. B 299 295Bentsson I 1989 Int. J. Mod. Phys. A 4 5527Bentsson I 1991 Class. Quantum Grav. 8 1847Varadarajan M 1991 Class. Quantum Grav. 8 L235[10] Ashtekar A, Romano J D and Tate R S 1989 Phys. Rev. D 40 2572Smolin L 2002 Quantum Gravity with a Positive Cosmological Constant arXiv:hep-th/0209079 |
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