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Circularly symmetric solutions in three-dimensional teleparallel, f (T ) and Maxwell-f (T ) gravity

  • P. A. González
  • Emmanuel N. Saridakis
  • Yerko Vásquez
Article

Abstract

We present teleparallel 3D gravity and we extract circularly symmetric solutions, showing that they coincide with the BTZ and Deser-de-Sitter solutions of standard 3D gravity. However, extending into f (T ) 3D gravity, that is considering arbitrary functions of the torsion scalar in the action, we obtain BTZ-like and Deser-de-Sitter-like solutions, corresponding to an effective cosmological constant, without any requirement of the sign of the initial cosmological constant. Finally, extending our analysis incorporating the electromagnetic sector, we show that Maxwell-f (T ) gravity accepts deformed charged BTZ-like solutions. Interestingly enough, the deformation in this case brings qualitatively novel terms, contrary to the pure gravitational solutions where the deformation is expressed only through changes in the coefficients. We investigate the singularities and the horizons of the new solutions, and amongst others we show that the cosmic censorship can be violated. Such novel behaviors reveal the new features that the f (T ) structure brings in 3D gravity.

Keywords

2D Gravity Black Holes Classical Theories of Gravity 

References

  1. [1]
    M. Bañados, C. Teitelboim and J. Zanelli, The black hole in three-dimensional space-time, Phys. Rev. Lett. 69 (1992) 1849 [hep-th/9204099] [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  2. [2]
    S. Carlip, The (2 + 1)-dimensional black hole, Class. Quant. Grav. 12 (1995) 2853 [gr-qc/9506079] [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  3. [3]
    S. Carlip, Conformal field theory, (2 + 1)-dimensional gravity and the BTZ black hole, Class. Quant. Grav. 22 (2005) R85 [gr-qc/0503022] [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  4. [4]
    S. Deser, R. Jackiw and S. Templeton, Topologically massive gauge theories, Annals Phys. 140 (1982) 372 [Erratum ibid. 185 (1988) 406] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  5. [5]
    S. Deser, R. Jackiw and S. Templeton, Three-dimensional massive gauge theories, Phys. Rev. Lett. 48 (1982) 975 [INSPIRE].ADSCrossRefGoogle Scholar
  6. [6]
    W. Li, W. Song and A. Strominger, Chiral gravity in three dimensions, JHEP 04 (2008) 082 [arXiv:0801.4566] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  7. [7]
    A. Strominger, A simple proof of the chiral gravity conjecture, arXiv:0808.0506 [INSPIRE].
  8. [8]
    S. Carlip, S. Deser, A. Waldron and D. Wise, Cosmological topologically massive gravitons and photons, Class. Quant. Grav. 26 (2009) 075008 [arXiv:0803.3998] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  9. [9]
    S. Carlip, S. Deser, A. Waldron and D. Wise, Topologically massive AdS gravity, Phys. Lett. B 666 (2008) 272 [arXiv:0807.0486] [INSPIRE].MathSciNetADSGoogle Scholar
  10. [10]
    S. Carlip, The constraint algebra of topologically massive AdS gravity, JHEP 10 (2008) 078 [arXiv:0807.4152] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    G. Giribet, M. Kleban and M. Porrati, Topologically massive gravity at the chiral point is not chiral, JHEP 10 (2008) 045 [arXiv:0807.4703] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  12. [12]
    M.-i. Park, Constraint dynamics and gravitons in three dimensions, JHEP 09 (2008) 084 [arXiv:0805.4328] [INSPIRE].Google Scholar
  13. [13]
    M. Blagojevic and B. Cvetkovic, Canonical structure of topologically massive gravity with a cosmological constant, JHEP 05 (2009) 073 [arXiv:0812.4742] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  14. [14]
    D. Grumiller, R. Jackiw and N. Johansson, Canonical analysis of cosmological topologically massive gravity at the chiral point, arXiv:0806.4185 [INSPIRE].
  15. [15]
    A. Garbarz, G. Giribet and Y. Vasquez, Asymptotically AdS 3 solutions to topologically massive gravity at special values of the coupling constants, Phys. Rev. D 79 (2009) 044036 [arXiv:0811.4464] [INSPIRE].MathSciNetADSGoogle Scholar
  16. [16]
    D. Grumiller and N. Johansson, Instability in cosmological topologically massive gravity at the chiral point, JHEP 07 (2008) 134 [arXiv:0805.2610] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    D. Grumiller and N. Johansson, Consistent boundary conditions for cosmological topologically massive gravity at the chiral point, Int. J. Mod. Phys. D 17 (2009) 2367 [arXiv:0808.2575] [INSPIRE].MathSciNetADSGoogle Scholar
  18. [18]
    M. Henneaux, C. Martinez and R. Troncoso, Asymptotically Anti-de Sitter spacetimes in topologically massive gravity, Phys. Rev. D 79 (2009) 081502 [arXiv:0901.2874] [INSPIRE].MathSciNetGoogle Scholar
  19. [19]
    A. Maloney, W. Song and A. Strominger, Chiral gravity, log gravity and extremal CFT, Phys. Rev. D 81 (2010) 064007 [arXiv:0903.4573] [INSPIRE].MathSciNetADSGoogle Scholar
  20. [20]
    E. Ayon-Beato, A. Garbarz, G. Giribet and M. Hassaine, Lifshitz black hole in three dimensions, Phys. Rev. D 80 (2009) 104029 [arXiv:0909.1347] [INSPIRE].MathSciNetADSGoogle Scholar
  21. [21]
    A. Unzicker and T. Case, Translation of Einsteins attempt of a unified field theory with teleparallelism, physics/0503046 [INSPIRE].
  22. [22]
    K. Hayashi and T. Shirafuji, New general relativity, Phys. Rev. D 19 (1979) 3524 [Addendum ibid. D 24 (1982) 3312-3314] [INSPIRE].MathSciNetADSGoogle Scholar
  23. [23]
    T. Kawai, Teleparallel theory of (2 + 1)-dimensional gravity, Phys. Rev. D 48 (1993) 5668 .ADSGoogle Scholar
  24. [24]
    T. Kawai, Exotic black hole solution in teleparallel theory of (2 + 1) dimensional gravity, Prog. Theor. Phys. 94 (1995) 1169 [gr-qc/9410032] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    T. Kawai, Generators of internal Lorentz transformations and of general affine coordinate transformations in teleparallel theory of (2 + 1)-dimensional gravity. Cases with static circularly symmetric space times, Prog. Theor. Phys. 94 (1995) 915 [gr-qc/9507017] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    E.W. Mielke and P. Baekler, Topological gauge model of gravity with torsion, Phys. Lett. A 156 (1991) 399 [INSPIRE].MathSciNetADSGoogle Scholar
  27. [27]
    A. Sousa and J. Maluf, Black holes in 2 + 1 teleparallel theories of gravity, Prog. Theor. Phys. 108 (2002) 457 [gr-qc/0301079] [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  28. [28]
    A.A. Garcia, F.W. Hehl, C. Heinicke and A. Macias, Exact vacuum solution of a (1 + 2)-dimensional Poincaré gauge theory: BTZ solution with torsion, Phys. Rev. D 67 (2003) 124016 [gr-qc/0302097] [INSPIRE].MathSciNetADSGoogle Scholar
  29. [29]
    M. Blagojevic and B. Cvetkovic, Electric field in 3D gravity with torsion, Phys. Rev. D 78 (2008) 044036 [arXiv:0804.1899] [INSPIRE].MathSciNetADSGoogle Scholar
  30. [30]
    M. Blagojevic and B. Cvetkovic, Self-dual Maxwell field in 3D gravity with torsion, Phys. Rev. D 78 (2008) 044037 [arXiv:0805.3627] [INSPIRE].MathSciNetADSGoogle Scholar
  31. [31]
    M. Blagojevic, B. Cvetkovic and O. Mišković, Nonlinear electrodynamics in 3D gravity with torsion, Phys. Rev. D 80 (2009) 024043 [arXiv:0906.0235] [INSPIRE].ADSGoogle Scholar
  32. [32]
    Y. Vasquez, Exact solutions in 3D gravity with torsion, JHEP 08 (2011) 089 [arXiv:0907.4165] [INSPIRE].MathSciNetGoogle Scholar
  33. [33]
    R.C. Santamaria, J.D. Edelstein, A. Garbarz and G.E. Giribet, On the addition of torsion to chiral gravity, Phys. Rev. D 83 (2011) 124032 [arXiv:1102.4649] [INSPIRE].ADSGoogle Scholar
  34. [34]
    R. Ferraro and F. Fiorini, Modified teleparallel gravity: inflation without inflaton, Phys. Rev. D 75 (2007) 084031 [gr-qc/0610067] [INSPIRE].MathSciNetADSGoogle Scholar
  35. [35]
    R. Ferraro and F. Fiorini, On Born-Infeld gravity in Weitzenbock spacetime, Phys. Rev. D 78 (2008) 124019 [arXiv:0812.1981] [INSPIRE].MathSciNetADSGoogle Scholar
  36. [36]
    G.R. Bengochea and R. Ferraro, Dark torsion as the cosmic speed-up, Phys. Rev. D 79 (2009) 124019 [arXiv:0812.1205] [INSPIRE].ADSGoogle Scholar
  37. [37]
    E.V. Linder, Einsteins other gravity and the acceleration of the universe, Phys. Rev. D 81 (2010) 127301 [Erratum ibid. D 82 (2010) 109902] [arXiv:1005.3039] [INSPIRE].ADSGoogle Scholar
  38. [38]
    R. Myrzakulov, Accelerating universe from F (T ) gravity, Eur. Phys. J. C 71 (2011) 1752 [arXiv:1006.1120] [INSPIRE].ADSCrossRefGoogle Scholar
  39. [39]
    S.-H. Chen, J.B. Dent, S. Dutta and E.N. Saridakis, Cosmological perturbations in F (T ) gravity, Phys. Rev. D 83 (2011) 023508 [arXiv:1008.1250] [INSPIRE].ADSGoogle Scholar
  40. [40]
    P. Wu and H.W. Yu, f (T ) models with phantom divide line crossing, Eur. Phys. J. C 71 (2011) 1552 [arXiv:1008.3669] [INSPIRE].ADSGoogle Scholar
  41. [41]
    K. Bamba, C.-Q. Geng and C.-C. Lee, Comment onEinsteins other gravity and the acceleration of the universe”, arXiv:1008.4036 [INSPIRE].
  42. [42]
    J.B. Dent, S. Dutta and E.N. Saridakis, f (T ) gravity mimicking dynamical dark energy. Background and perturbation analysis, JCAP 01 (2011) 009 [arXiv:1010.2215] [INSPIRE].ADSCrossRefGoogle Scholar
  43. [43]
    R. Zheng and Q.-G. Huang, Growth factor in f (T ) gravity, JCAP 03 (2011) 002 [arXiv:1010.3512] [INSPIRE].ADSCrossRefGoogle Scholar
  44. [44]
    K. Bamba, C.-Q. Geng, C.-C. Lee and L.-W. Luo, Equation of state for dark energy in f (T ) gravity, JCAP 01 (2011) 021 [arXiv:1011.0508] [INSPIRE].ADSCrossRefGoogle Scholar
  45. [45]
    K. Yerzhanov, S. Myrzakul, I. Kulnazarov and R. Myrzakulov, Accelerating cosmology in f (T ) gravity with scalar field, arXiv:1006.3879 [INSPIRE].
  46. [46]
    R.-J. Yang, Conformal transformation in f (T ) theories, Europhys. Lett. 93 (2011) 60001 [arXiv:1010.1376] [INSPIRE].ADSCrossRefGoogle Scholar
  47. [47]
    P. Wu and H.W. Yu, Observational constraints on f (T ) theory, Phys. Lett. B 693 (2010) 415 [arXiv:1006.0674] [INSPIRE].MathSciNetADSGoogle Scholar
  48. [48]
    G.R. Bengochea, Observational information for f (T ) theories and dark torsion, Phys. Lett. B 695 (2011) 405 [arXiv:1008.3188] [INSPIRE].ADSGoogle Scholar
  49. [49]
    P. Wu and H.W. Yu, The dynamical behavior of f (T ) theory, Phys. Lett. B 692 (2010) 176 [arXiv:1007.2348] [INSPIRE].MathSciNetADSGoogle Scholar
  50. [50]
    Y. Zhang, H. Li, Y. Gong and Z.-H. Zhu, Notes on f (T ) theories, JCAP 07 (2011) 015 [arXiv:1103.0719] [INSPIRE].ADSCrossRefGoogle Scholar
  51. [51]
    R. Ferraro and F. Fiorini, Non trivial frames for f (T ) theories of gravity and beyond, Phys. Lett. B 702 (2011) 75 [arXiv:1103.0824] [INSPIRE].MathSciNetADSGoogle Scholar
  52. [52]
    Y.-F. Cai, S.-H. Chen, J.B. Dent, S. Dutta and E.N. Saridakis, Matter bounce cosmology with the f (T ) gravity, Class. Quant. Grav. 28 (2011) 215011 [arXiv:1104.4349] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  53. [53]
    S. Chattopadhyay and U. Debnath, Emergent universe in chameleon, f (R) and f (T ) gravity theories, Int. J. Mod. Phys. D 20 (2011) 1135 [arXiv:1105.1091] [INSPIRE].ADSGoogle Scholar
  54. [54]
    M. Sharif and S. Rani, f (T ) models within Bianchi type I universe, Mod. Phys. Lett. A 26 (2011) 1657 [arXiv:1105.6228] [INSPIRE].MathSciNetADSGoogle Scholar
  55. [55]
    H. Wei, X.-P. Ma and H.-Y. Qi, f (T ) theories and varying fine structure constant, Phys. Lett. B 703 (2011) 74 [arXiv:1106.0102] [INSPIRE].ADSGoogle Scholar
  56. [56]
    R. Ferraro and F. Fiorini, Cosmological frames for theories with absolute parallelism, Int. J. Mod. Phys. Conf. Ser. 3 (2011) 227 [arXiv:1106.6349] [INSPIRE].CrossRefGoogle Scholar
  57. [57]
    C.G. Boehmer, A. Mussa and N. Tamanini, Existence of relativistic stars in f (T ) gravity, Class. Quant. Grav. 28 (2011) 245020 [arXiv:1107.4455] [INSPIRE].ADSCrossRefGoogle Scholar
  58. [58]
    H. Wei, H.-Y. Qi and X.-P. Ma, Constraining f (T ) theories with the varying gravitational constant, arXiv:1108.0859 [INSPIRE].
  59. [59]
    S. Capozziello, V. Cardone, H. Farajollahi and A. Ravanpak, Cosmography in f (T )-gravity, Phys. Rev. D 84 (2011) 043527 [arXiv:1108.2789] [INSPIRE].ADSGoogle Scholar
  60. [60]
    P. Wu and H. Yu, The stability of the Einstein static state in f (T ) gravity, Phys. Lett. B 703 (2011) 223 [arXiv:1108.5908] [INSPIRE].MathSciNetADSGoogle Scholar
  61. [61]
    M.H. Daouda, M.E. Rodrigues and M. Houndjo, Static anisotropic solutions in f (T ) theory, Eur. Phys. J. C 72 (2012) 1890 [arXiv:1109.0528] [INSPIRE].ADSCrossRefGoogle Scholar
  62. [62]
    M. Hamani Daouda, M.E. Rodrigues and M. Houndjo, New static solutions in f (T ) theory, Eur. Phys. J. C 71 (2011) 1817 [arXiv:1108.2920] [INSPIRE].ADSCrossRefGoogle Scholar
  63. [63]
    K. Bamba and C.-Q. Geng, Thermodynamics of cosmological horizons in f (T ) gravity, JCAP 11 (2011) 008 [arXiv:1109.1694] [INSPIRE].ADSCrossRefGoogle Scholar
  64. [64]
    C.-Q. Geng, C.-C. Lee, E.N. Saridakis and Y.-P. Wu, ’teleparalleldark energy, Phys. Lett. B 704 (2011) 384 [arXiv:1109.1092] [INSPIRE].ADSGoogle Scholar
  65. [65]
    H. Wei, Dynamics of teleparallel dark energy, Phys. Lett. B 712 (2012) 430 [arXiv:1109.6107] [INSPIRE].ADSGoogle Scholar
  66. [66]
    C.-Q. Geng, C.-C. Lee and E.N. Saridakis, Observational constraints on teleparallel dark energy, JCAP 01 (2012) 002 [arXiv:1110.0913] [INSPIRE].ADSCrossRefGoogle Scholar
  67. [67]
    C. Xu, E.N. Saridakis and G. Leon, Phase-space analysis of teleparallel dark energy, arXiv:1202.3781 [INSPIRE].
  68. [68]
    L. Iorio and E.N. Saridakis, Solar system constraints on f (T ) gravity, arXiv:1203.5781 [INSPIRE].
  69. [69]
    T. Wang, Static solutions with spherical symmetry in f (T ) theories, Phys. Rev. D 84 (2011) 024042 [arXiv:1102.4410] [INSPIRE].ADSGoogle Scholar
  70. [70]
    R.-X. Miao, M. Li and Y.-G. Miao, Violation of the first law of black hole thermodynamics in f (T ) gravity, JCAP 11 (2011) 033 [arXiv:1107.0515] [INSPIRE].ADSCrossRefGoogle Scholar
  71. [71]
    H. Wei, X.-J. Guo and L.-F. Wang, Noether symmetry in f (T ) theory, Phys. Lett. B 707 (2012) 298 [arXiv:1112.2270] [INSPIRE].ADSGoogle Scholar
  72. [72]
    R. Ferraro and F. Fiorini, Spherically symmetric static spacetimes in vacuum f (T ) gravity, Phys. Rev. D 84 (2011) 083518 [arXiv:1109.4209] [INSPIRE].ADSGoogle Scholar
  73. [73]
    R. Weitzenböck , Invarianten Theorie, Nordhoff, Groningen The Netherlands (1923).Google Scholar
  74. [74]
    J. Maluf, Hamiltonian formulation of the teleparallel description of general relativity, J. Math. Phys. 35 (1994) 335 [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  75. [75]
    H. Arcos and J. Pereira, Torsion gravity: a reappraisal, Int. J. Mod. Phys. D 13 (2004) 2193 [gr-qc/0501017] [INSPIRE].MathSciNetADSGoogle Scholar
  76. [76]
    S. Weinberg, Cosmology, Oxford University Press, Oxford U.K. (2008).MATHGoogle Scholar
  77. [77]
    U. Muench, F. Gronwald and F.W. Hehl, A small guide to variations in teleparallel gauge theories of gravity and the Kaniel-Itin model, Gen. Rel. Grav. 30 (1998) 933 [gr-qc/9801036] [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  78. [78]
    Y. Itin, Coframe teleparallel models of gravity: exact solutions, Int. J. Mod. Phys. D 10 (2001) 547 [gr-qc/9912013] [INSPIRE].MathSciNetADSGoogle Scholar
  79. [79]
    S. Deser, R. Jackiw and G. ’t Hooft, Three-dimensional Einstein gravity: dynamics of flat space, Annals Phys. 152 (1984) 220 [INSPIRE].ADSCrossRefGoogle Scholar
  80. [80]
    T.P. Sotiriou, B. Li and J.D. Barrow, Generalizations of teleparallel gravity and local Lorentz symmetry, Phys. Rev. D 83 (2011) 104030 [arXiv:1012.4039] [INSPIRE].ADSGoogle Scholar
  81. [81]
    B. Li, T.P. Sotiriou and J.D. Barrow, Large-scale structure in f (T ) gravity, Phys. Rev. D 83 (2011) 104017 [arXiv:1103.2786] [INSPIRE].ADSGoogle Scholar
  82. [82]
    M. Li, R.-X. Miao and Y.-G. Miao, Degrees of freedom of f (T ) gravity, JHEP 07 (2011) 108 [arXiv:1105.5934] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  83. [83]
    Y.-F. Cai, S.-H. Chen, J.B. Dent, S. Dutta, E.N. Saridakis, in preparation.Google Scholar
  84. [84]
    M. Cataldo, Azimuthal electric field in a static rotationally symmetric (2 + 1)-dimensional space-time, Phys. Lett. B 529 (2002) 143 [gr-qc/0201047] [INSPIRE].MathSciNetADSGoogle Scholar
  85. [85]
    P. Painlevé, La mécanique classique et la théorie de la relativité, C. R. Acad. Sci. Paris 173 (1921) 677.MATHGoogle Scholar
  86. [86]
    A. Gullstrand, Allegemeine Lösung des statischen Einkörper-problems in der Einsteinschen Gravitations theorie, Arkiv. Mat. Astron. Fys. 16 (1922) 1.Google Scholar
  87. [87]
    K. Martel and E. Poisson, Regular coordinate systems for Schwarzschild and other spherical space-times, Am. J. Phys. 69 (2001) 476 [gr-qc/0001069] [INSPIRE].ADSCrossRefGoogle Scholar
  88. [88]
    W. Liu, New coordinates for BTZ black hole and Hawking radiation via tunnelling, Phys. Lett. B 634 (2006) 541 [gr-qc/0512099] [INSPIRE].ADSGoogle Scholar
  89. [89]
    R. Courant and D. Hilbert, Methods of mathematical physics, vol. 2, Cambridge University Press, Cambridge U.K. (1966).Google Scholar
  90. [90]
    A. Peres, PP waves, Phys. Rev. Lett. 3 (1959) 571 [hep-th/0205040] [INSPIRE].ADSMATHCrossRefGoogle Scholar
  91. [91]
    K. Skenderis and M. Taylor, Branes in AdS and pp wave space-times, JHEP 06 (2002) 025 [hep-th/0204054] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  92. [92]
    E. Ayon-Beato and M. Hassaine, PP waves of conformal gravity with self-interacting source, Annals Phys. 317 (2005) 175 [hep-th/0409150] [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  93. [93]
    A. de la Cruz-Dombriz, A. Dobado and A. Maroto, Black holes in f (R) theories, Phys. Rev. D 80 (2009) 124011 [Erratum ibid. D 83 (2011) 029903] [arXiv:0907.3872] [INSPIRE].ADSGoogle Scholar
  94. [94]
    D.H. Park and S.H. Yang, Geodesic motions in (2 + 1)-dimensional charged black holes, Gen. Rel. Grav. 31 (1999) 1343 [gr-qc/9901027] [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  95. [95]
    S. Hendi, Charged BTZ-like black holes in higher dimensions, Eur. Phys. J. C 71 (2011) 1551 [arXiv:1007.2704] [INSPIRE].ADSGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2012

Authors and Affiliations

  • P. A. González
    • 1
    • 2
  • Emmanuel N. Saridakis
    • 3
  • Yerko Vásquez
    • 4
  1. 1.Escuela de Ingenierıa Civil en Obras Civiles, Facultad de Ciencias F´ısicas y MatemáticasUniversidad Central de ChileSantiagoChile
  2. 2.Universidad Diego PortalesSantiagoChile
  3. 3.CASPER, Physics DepartmentBaylor UniversityWacoU.S.A.
  4. 4.Departamento de Ciencias Fısicas, Facultad de Ingenier´ıa, Ciencias y AdministraciónUniversidad de La FronteraCasillaChile

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