Birkhoffs theorem for three-dimensional ads gravity

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Ayón-Beato, Eloy; Martínez, Cristián; Zanelli, Jorge;
  • Related identifiers: doi: 10.1103/PhysRevD.70.044027
  • Subject: High Energy Physics - Theory
    arxiv: General Relativity and Quantum Cosmology

All three-dimensional matter-free spacetimes with negative cosmological constant, compatible with cyclic symmetry are identified. The only cyclic solutions are the 2+1 (BTZ) black hole with SO(2) x R isometry, and the self-dual Coussaert-Henneaux spacetimes, with isomet... View more
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    22 references, page 1 of 3

    Degenerate case: c33 = 0 If the fields KF1,T1 and KF2,T2 are null (c11 = 0) and spacelike (c22 > 0) respectively, they span a null plane (case III above). In this case c33 = 0, and therefore KF1,T1 , KF2,T2 and [KF1,T1 , KF2,T2 ] are not linearly independent. However, it is possible to find another independent null Killing vector which, together with KF1,T1 and KF2,T2 , generate the same so(2, 1) algebra. Without loss of generality they KF1,T1 and KF2,T2 can be taken to be orthogonal (c12 = 0), and their commutator is not linearly independent, but is given by

    [1] J. D. Brown, Lower Dimensional Gravity (World Scientific, Singapore 1988).

    [2] S. Carlip, Quantum Gravity in 2 + 1 Dimensions (Cambridge Univ. Press, Cambridge 1998).

    [3] M. Ban˜ados, C. Teitelboim, and J. Zanelli, Phys. Rev. Lett. 69, 1849 (1992) [arXiv:hep-th/9204099].

    [4] M. Ban˜ados, M. Henneaux, C. Teitelboim, and J. Zanelli Phys. Rev. D 48, 1506 (1993) [arXiv:gr-qc/9302012].

    [5] S. Aminneborg, I. Bengtsson, S. Holst and P. Peldan, Class. Quant. Grav. 13, 2707 (1996) [arXiv:grqc/9604005].

    [6] S. Holst and P. Peldan, Class. Quant. Grav. 14, 3433 (1997) [arXiv:gr-qc/9705067].

    [7] M. Ban˜ados, Phys. Rev. D 57, 1068 (1998) [arXiv:grqc/9703040].

    [8] M. Ban˜ados, A. Gomberoff and C. Mart´ınez, Class. Quant. Grav. 15, 3575 (1998) [arXiv:hep-th/9805087].

    [9] O. Madden and S. F. Ross, arXiv:hep-th/0401205.

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