Transactions in Theoretical and Mathematical Physics

Transactions in Theoretical and Mathematical Physics

(2+1)-dimensional Chern-Simons bi-gravity with AdS Lie bialgebra as an interacting theory of two massless spin-2 fields

Document Type : Original Article

Authors
1 Azarbaijan shahid Madani university
2 Department of Physics, Faculty of Science, Azarbaijan Shahid Madani University, 53714-161, Tabriz, Iran
Abstract
We introduce a new Lie bialgebra structure for the anti de Sitter (AdS) Lie algebra in (2+1)-dimensional spacetime. By gauging the resulting \textit{AdS Lie bialgebra}, we write a Chern-Simons gauge theory of bi-gravity involving two dreibeins rather than two metrics, which describes two interacting massless spin-2 fields. Our ghost-free bi-gravity model which has no any local degrees of freedom, has also a suitable free field limit. By solving its equations of motion, we obtain a \textit{new black hole} solution which has two curvature singularities and two horizons. We also study cosmological implications of this massless bi-gravity model.
Keywords
Subjects

1. E. Witten, Nucl. Phys. B311, (1988/89)#

2. S. Carlip, J. Korean Phys. Soc. 28, (1995)#

3. S. Carlip, Living Rev. Rel. 8, (2005)#

4. S. Carlip, Class. Quant. Grav. 22, (2005)#

5. E. Witten, [arXiv:0706.3359[hep-th]], (2007)#

6. N. Boulanger, T. Damour, L. Gualtieri, M. Henneaux,
Nucl.Phys. B597, (2001)#

7. N. Boulanger, L. Gualtieri, Class. Quant. Grav. 18,
(2001)#

8. K. Hinterbichler, Rev. Mod. Phys. 84, (2012)#

9. C. de Rham, Living Rev. Relativity 17, (2014)#

10. S. Deser, R. Jackiw, S. Templeton, Annals Phys. 140,
(1982)#

11. S. Deser, R. Jackiw, S. Templeton, Phys. Rev. Lett.
48, (1982)#

12. S. Carlip, JHEP 0810, (2008)#

13. M. Blagojevic, B. Cvetkovic, JHEP 0905, (2009)#

14. E. A. Bergshoeff, O. Hohm, P. K. Townsend, Phys.
Rev. Lett. 102, (2009)#

15. E. A. Bergshoeff, O. Hohm, P. K. Townsend, Phys.
Rev. D79, (2009)#

16. M. Blagojevic, B. Cvetkovic, JHEP 1101, (2011)#

17. O. Hohm, A. Routh, P. K. Townsend, B. Zhang, Phys.
Rev. D86, (2012)#

18. C. de Rham, G. Gabadadze, Phys. Rev. D82, (2010)#

19. C. de Rham, G. Gabadadze, A. J. Tolley, Phys. Rev.
Lett. 106, (2011)#

20. S.F. Hassan, R.A. Rosen, JHEP 1107, (2011)#

21. W. Merbis, PhD thesis defended at the University of
Groningen, (2014)#

22. E.A. Bergshoeff, S. de Haan, O. Hohm, W. Merbis,
P.K. Townsend, Phys. Rev. Lett. 111, (2013)#

23. E.A. Bergshoeff, A.F. Goya, W. Merbis, J. Rosseel,
JHEP 1404 (2014)#

24. S.F. Hassan, R.A. Rosen, JHEP 1202, (2012)#

25. K. Hinterbichler, R.A. Rosen, JHEP 1207, (2012)#

26. E. Bergshoeff, O. Hohm,W. Merbis, A.J. Routh, P.K.
Townsend, Lect. Notes Phys. 892, (2015)#

27. M.R. Setare, H. Adami, Phys. Lett. B750, (2015)#

28. H. Bacry, P. Combe, J.L. Richard, Nuovo Cim. A67,
(1970)#

29. R. Schrader, Fortsch. Phys. 20, (1972)#

30. J.A. de Azcarraga, K. Kamimura, J. Lukierski, Phys.
Rev. D83, (2011)#

31. J.A. de Azcarraga, K. Kamimura, J. Lukierski, Int. J.
Mod. Phys. Conf. Ser. 23 (2013)#

32. P. Salgado, R.J. Szabo, O. Valdivia, Phys. Rev. D89,
(2014)#

33. O. Cebecioğlu, S. Kibaroğlu, Phys. Rev. D90, (2014)#

34. O. Cebecioğlu, S. Kibaroğlu, Phys. Lett. B751, (2015)
35. S. Hoseinzadeh, A. Rezaei-Aghdam, Phys. Rev. D90,
(2014)#

36. D.V. Soroka, V.A. Soroka, Phys. Lett. B707, (2012)#

37. J. Díaz, O. Fierro, F. Izaurieta, N. Merino, E. Ro
driguez, P. Salgado, O. Valdivia, J. Phys. A45, (2012)#

38. S. Hoseinzadeh, A. Rezaei-Aghdam, Eur. Phys. J.
C75, (2015)#

39. S.
Hoseinzadeh,
A.
[arXiv:1705.11042[hep-th]], (2017)
Rezaei-Aghdam,#

40. V. Chari, A. Pressley, A Guide to Quantum Groups,
Cambridge Univ. Press (1994)#

41. A. Rezaei-Aghdam, M. Hemmati, A.R. Rastkar, J.
Phys. A: Math. Gen. 38, (2005)#

42. C.R. Nappi, E. Witten, Phys. Rev. Lett. 71, (1993)#

43. M. Bañados, C. Teitelboim, J. Zanelli, Phys. Rev. Lett.
69, (1992); M. Bañados, M. Henneaux, C. Teitelboim,
J. Zanelli, Phys. Rev. D48, (1993)#

44. M. Bañados, S. Theisen, JHEP 0911, (2009)#

45. H.R. Afshar, M. Alishahiha, A. Naseh, Phys. Rev.
D81, (2010)#
 
Volume 2, Issue 1
Winter 2025
Pages 22-29

  • Receive Date 11 February 2025
  • Accept Date 26 February 2025
  • First Publish Date 26 February 2025
  • Publish Date 01 February 2025