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Energy nonconservation as a link between f(R,T) gravity and noncommutative quantum theory

  • Ronaldo V. LobatoEmail author
  • G. A. Carvalho
  • A. G. Martins
  • P. H. R. S. Moraes
Regular Article

Abstract.

f (R, T) gravity was proposed as an extension of the f(R) theories, containing not just geometrical correction terms to the General Relativity equations, but also material correction terms, dependent on the trace of the energy-momentum tensor T . These material extra terms prevent the energy-momentum tensor of the theory from being conserved, even in a flat background. Energy nonconservation is a prediction of quantum theory with time-space noncommutativity. If time is considered as an operator and there are compact spatial coordinates which do not commute with time, then the time evolution gets quantized and energy conservation can be violated. In the present work we construct a model in a 5-dimensional flat spacetime consisting of 3 commutative spatial dimensions and 1 compact spatial dimension whose coordinate does not commute with time. We show that energy flows from the 3-dimensional commutative slice into the compact extra dimension (and vice versa), so that conservation of energy is restored. In this model the energy flux is proportional to the energy density of the matter content, leading to a differential equation for f(R,T), thus providing a physical criterion to restrict the functional form of f(R,T). We solve this equation and analyze the behavior of its solution in a spherically symmetric context.

References

  1. 1.
    J. Neveu, V. Ruhlmann-Kleider, P. Astier, M. Besançon, J. Guy, A. Möller, E. Babichev, Astron. Astrophys. 600, A40 (2017)ADSCrossRefGoogle Scholar
  2. 2.
    John D. Barrow, Roy Maartens, Christos G. Tsagas, Phys. Rep. 449, 131 (2007)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    T.S.V. Albada, R. Sancisi, M. Petrou, R.J. Tayler, Philos. Trans. R. Soc. A 320, 447 (1986)ADSCrossRefGoogle Scholar
  4. 4.
    R.A. Swaters, B.F. Madore, M. Trewhella, Astrophys. J. 531, L107 (2000)ADSCrossRefGoogle Scholar
  5. 5.
    Antonino Del Popolo, Morgan Le Delliou, Galaxies 5, 17 (2017)ADSCrossRefGoogle Scholar
  6. 6.
    Thomas P. Sotiriou, Valerio Faraoni, Rev. Mod. Phys. 82, 451 (2010)ADSCrossRefGoogle Scholar
  7. 7.
    S. Nojiri, S.D. Odintsov, V.K. Oikonomou, Phys. Rep. 692, 1 (2017)ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    S. Capozziello, P. Martin-Moruno, C. Rubano, Phys. Lett. B 664, 12 (2008)ADSCrossRefGoogle Scholar
  9. 9.
    Shin’ichi Nojiri, Sergei D. Odintsov, Phys. Rev. D 68, 123512 (2003)ADSCrossRefGoogle Scholar
  10. 10.
    Shin’ichi Nojiri, Sergei D. Odintsov, Phys. Lett. B 657, 238 (2007)ADSCrossRefGoogle Scholar
  11. 11.
    Thomas P. Sotiriou, J. Phys.: Conf. Ser. 189, 012039 (2009)Google Scholar
  12. 12.
    S. Nojiri, S.D. Odintsov, Int. J. Geom. Methods Mod. Phys. 04, 115 (2007)CrossRefGoogle Scholar
  13. 13.
    Tiberiu Harko, Francisco S.N. Lobo, Shin’ichi Nojiri, Sergei D. Odintsov, Phys. Rev. D 84, 024020 (2011)ADSCrossRefGoogle Scholar
  14. 14.
    Sergei D. Odintsov, Diego Sáez-Gómez, Phys. Lett. B 725, 437 (2013)ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    Xue-Mei Deng, Yi Xie, Int. J. Theor. Phys. 54, 1739 (2015)CrossRefGoogle Scholar
  16. 16.
    Hamid Shabani, Mehrdad Farhoudi, Phys. Rev. D 90, 044031 (2014)ADSCrossRefGoogle Scholar
  17. 17.
    P.H.R.S. Moraes, José D.V. Arbañil, M. Malheiro, J. Cosmol. Astropart. Phys. 2016, 005 (2016)CrossRefGoogle Scholar
  18. 18.
    G.A. Carvalho, R.V. Lobato, P.H.R.S. Moraes, José D.V. Arbañil, E. Otoniel, R.M. Marinho, M. Malheiro, Eur. Phys. J. C 77, 871 (2017)ADSCrossRefGoogle Scholar
  19. 19.
    M. Sharif, Aisha Siddiqa, Eur. Phys. J. Plus 132, 529 (2017)CrossRefGoogle Scholar
  20. 20.
    R. Jackiw, Nucl. Phys. B - Proc. Suppl. 108, 30 (2002)ADSCrossRefGoogle Scholar
  21. 21.
    Hartland S. Snyder, Phys. Rev. 71, 38 (1947)ADSCrossRefGoogle Scholar
  22. 22.
    Richard J. Szabo, Phys. Rep. 378, 207 (2003)ADSMathSciNetCrossRefGoogle Scholar
  23. 23.
    M. Chaichian, A. Demichev, P. Prešnajder, Nucl. Phys. B 567, 360 (2000)ADSCrossRefGoogle Scholar
  24. 24.
    Sergio Doplicher, Klaus Fredenhagen, John E. Roberts, Commun. Math. Phys. 172, 187 (1995)ADSCrossRefGoogle Scholar
  25. 25.
    Alain Connes, Michael R. Douglas, Albert Schwarz, J. High Energy Phys. 1998, 003 (1998)CrossRefGoogle Scholar
  26. 26.
    Nathan Seiberg, Edward Witten, J. High Energy Phys. 1999, 032 (1999)CrossRefGoogle Scholar
  27. 27.
    Piero Nicolini, Int. J. Mod. Phys. A 24, 1229 (2008)CrossRefGoogle Scholar
  28. 28.
    Piero Nicolini, Anais Smailagic, Euro Spallucci, Phys. Lett. B 632, 547 (2006)MathSciNetCrossRefGoogle Scholar
  29. 29.
    S. Hamid Mehdipour, Eur. Phys. J. Plus 127, 80 (2012)CrossRefGoogle Scholar
  30. 30.
    M. Sharif, Shamaila Rani, Phys. Rev. D 88, 123501 (2013)ADSCrossRefGoogle Scholar
  31. 31.
    F. Rahaman, Saibal Ray, G.S. Khadekar, P.K.F. Kuhfittig, I. Karar, Int. J. Theor. Phys. 54, 699 (2015)CrossRefGoogle Scholar
  32. 32.
    Ayan Banerjee, Sudan Hansraj, Eur. Phys. J. C 76, 641 (2016)ADSCrossRefGoogle Scholar
  33. 33.
    Ali Övgün, Ayan Banerjee, Kimet Jusufi, Eur. Phys. J. C 77, 566 (2017)ADSCrossRefGoogle Scholar
  34. 34.
    Mubasher Jamil, Farook Rahaman, Ratbay Myrzakulov, P.K.F. Kuhfittig, Nasr Ahmed, Umar F. Mondal, J. Korean Phys. Soc. 65, 917 (2013)CrossRefGoogle Scholar
  35. 35.
    M. Sharif, H. Ismat Fatima, Mod. Phys. Lett. A 30, 1550142 (2015)ADSCrossRefGoogle Scholar
  36. 36.
    Shamaila Rani, Abdul Jawad, Adv. High Energy Phys. 2016, 1 (2016)CrossRefGoogle Scholar
  37. 37.
    M. Sharif, Kanwal Nazir, Mod. Phys. Lett. A 32, 1750083 (2017)ADSCrossRefGoogle Scholar
  38. 38.
    B. Ducloué, L. Szymanowski, S. Wallon, Phys. Lett. B 738, 311 (2014)ADSCrossRefGoogle Scholar
  39. 39.
    Vittorio Del Duca, Carl R. Schmidt, Phys. Rev. D 51, 2150 (1995)CrossRefGoogle Scholar
  40. 40.
    Lynne H. Orr, W.J. Stirling, Phys. Rev. D 56, 5875 (1997)ADSCrossRefGoogle Scholar
  41. 41.
    J. Kwieciński, L. Motyka, Phys. Lett. B 462, 203 (1999)ADSCrossRefGoogle Scholar
  42. 42.
    V. Khachatryan et al., Phys. Rev. D 91, 092005 (2015)ADSMathSciNetCrossRefGoogle Scholar
  43. 43.
    Anindya Datta, Amitava Raychaudhuri, Avirup Shaw, Phys. Lett. B 730, 42 (2014)ADSMathSciNetCrossRefGoogle Scholar
  44. 44.
    Shin’ichi Nojiri, Sergei D. Odintsov, Phys. Rep. 505, 59 (2011)ADSMathSciNetCrossRefGoogle Scholar
  45. 45.
    Tiberiu Harko, Phys. Rev. D 90, 044067 (2014)ADSCrossRefGoogle Scholar
  46. 46.
    Tiberiu Harko, Francisco S.N. Lobo, José P. Mimoso, Diego Pavón, Eur. Phys. J. C 75, 386 (2015)ADSCrossRefGoogle Scholar
  47. 47.
    Xing Liu, Tiberiu Harko, Shi Dong Liang, Eur. Phys. J. C 76, 420 (2016)ADSCrossRefGoogle Scholar
  48. 48.
    Raziyeh Zaregonbadi, Mehrdad Farhoudi, Gen. Relativ. Gravit. 48, 142 (2016)CrossRefGoogle Scholar
  49. 49.
    Roberto Emparan, Harvey S. Reall, Living Rev. Relativ. 11, 6 (2008)ADSCrossRefGoogle Scholar
  50. 50.
    Shin’ichi Nojiri, Sergei D. Odintsov, Phys. Lett. B 599, 137 (2004)ADSCrossRefGoogle Scholar
  51. 51.
    Tiberiu Harko, Francisco S.N. Lobo, Eur. Phys. J. C 70, 373 (2010)ADSCrossRefGoogle Scholar
  52. 52.
    Shin’ichi Nojiri, Sergei D. Odintsov, Phys. Rev. D 81, 043001 (2010)ADSCrossRefGoogle Scholar
  53. 53.
    Tiberiu Harko, Francisco S.N. Lobo, Galaxies 2, 410 (2014)ADSCrossRefGoogle Scholar
  54. 54.
    Zahra Haghani, Tiberiu Harko, Francisco S.N. Lobo, Hamid Reza Sepangi, Shahab Shahidi, Phys. Rev. D 88, 044023 (2013)ADSCrossRefGoogle Scholar
  55. 55.
    Michael R. Douglas, Nikita A. Nekrasov, Rev. Mod. Phys. 73, 977 (2001)ADSCrossRefGoogle Scholar
  56. 56.
    Nathan Seiberg, Leonard Susskind, Nicolaos Toumbas, J. High Energy Phys. 2000, 044 (2000)CrossRefGoogle Scholar
  57. 57.
    M. Chaichian, A. Demichev, P. Prešnajder, A. Tureanu, Eur. Phys. J. C 20, 767 (2001)ADSCrossRefGoogle Scholar
  58. 58.
    Aiyalam P. Balachandran, Thupil R. Govindarajan, C. Molina, Paulo Teotonio-Sobrinho, J. High Energy Phys. 2004, 072 (2004)CrossRefGoogle Scholar
  59. 59.
    Aiyalam P. Balachandran, Thupil R. Govindarajan, Andrey Gomes Martins, Paulo Teotonio-Sobrinho, J. High Energy Phys. 2004, 068 (2004)CrossRefGoogle Scholar
  60. 60.
    Aiyalam P. Balachandran, Andrey Gomes Martins, Paulo Teotonio-Sobrinho, J. High Energy Phys. 2007, 066 (2007)ADSCrossRefGoogle Scholar
  61. 61.
    Brian C. Hall, An Elementary Introduction to Lie Groups, Lie Algebras, and Representations (Springer, New York, 2000)  https://doi.org/10.1007/978-0-387-21554-9
  62. 62.
    Hamid Shabani, Mehrdad Farhoudi, Phys. Rev. D 88, 044048 (2013)ADSCrossRefGoogle Scholar
  63. 63.
    Nima Arkani-Hamed, Savas Dimopoulos, Gia Dvali, Phys. Lett. B 429, 263 (1998)ADSCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Ronaldo V. Lobato
    • 1
    • 2
    • 3
    Email author
  • G. A. Carvalho
    • 1
    • 2
    • 3
  • A. G. Martins
    • 4
  • P. H. R. S. Moraes
    • 3
  1. 1.Dipartimento di Fisica and ICRASapienza Università di RomaRomeItaly
  2. 2.ICRANetPescaraItaly
  3. 3.Departamento de FísicaInstituto Tecnológico de AeronáuticaSão José dos CamposBrazil
  4. 4.Departamento de Ciências NaturaisUniversidade do Estado do ParáBelémBrazil

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