Skip to main content

Advertisement

SpringerLink
Log in

Conformal transformation route to gravity’s rainbow

  • Research Article
  • Published:
General Relativity and Gravitation Aims and scope Submit manuscript

Abstract

Conformal transformation as a mathematical tool has been used in many areas of gravitational physics. In this paper, we consider gravity’s rainbow, in which the metric can be treated as a conformal rescaling of the original metric. By using the conformal transformation technique, we get a specific form of a modified Newton’s constant and cosmological constant in gravity’s rainbow, which implies that the total vacuum energy is dependent on probe energy. Moreover, the result shows that Einstein gravity’s rainbow can be described by energy-dependent \(f(E,\tilde{R})\) gravity. At last, we study the f(R) gravity, when gravity’s rainbow is considered, which can also be described as energy-dependent \(\tilde{f}(E,\tilde{R})\) gravity.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Colladay, D., Kostelecký, V.A.: Lorentz-violating extension of the standard model. Phys. Rev. D 58, 116002 (1998)

    Article  ADS  Google Scholar 

  2. Coleman, S., Glashow, S.L.: High-energy tests of Lorentz invariance. Phys. Rev. D 59, 116008 (1999)

    Article  ADS  Google Scholar 

  3. Amelino-Camelia, G., Piran, T.: Planck-scale deformation of Lorentz symmetry as a solution to the ultrahigh energy cosmic ray and the TeV-photon paradoxes. Phys. Rev. D 64, 036005 (2001)

    Article  ADS  Google Scholar 

  4. Jacobson, T., Liberati, S., Mattingly, D.: TeV astrophysics constraints on Planck scale Lorentz violation. Phys. Rev. D 66, 081302 (2002)

    Article  ADS  Google Scholar 

  5. Myers, R.C., Pospelov, M.: Ultraviolet modifications of dispersion relations in effective field theory. Phys. Rev. Lett. 90, 211601 (2003)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  6. Jacobson, T., Liberati, S., Mattingly, D., Stecker, F.W.: New limits on planck scale lorentz violation in QED. Phys. Rev. Lett. 93, 021101 (2004)

    Article  ADS  Google Scholar 

  7. Magueijo, J., Smolin, L.: Lorentz invariance with an invariant energy scale. Phys. Rev. Lett. 88, 190403 (2002)

    Article  ADS  Google Scholar 

  8. Magueijo, J., Smolin, L.: Generalized Lorentz invariance with an invariant energy scale. Phys. Rev. D 67, 044017 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  9. Amelino-Camelia, G.: Testable scenario for relativity with minimum length. Phys. Lett. B 510(1), 255–263 (2001)

    Article  ADS  MATH  Google Scholar 

  10. Amelino-camelia, G.: Relativity in spacetimes with short-distance structure governed by an observer-independent (Planckian) length scale. Int. J. Mod. Phys. D 11(01), 35–59 (2002)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. Magueijo, J., Smolin, L.: Gravity’s rainbow. Class. Quantum. Gravit. 21(7), 1725 (2004)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. Garattini, R., Mandanici, G.: Modified dispersion relations lead to a finite zero point gravitational energy. Phys. Rev. D 83, 084021 (2011)

    Article  ADS  Google Scholar 

  13. Li, H., Ling, Y., Han, X.: Modified (A)dS Schwarzschild black holes in rainbow spacetime. Class. Quantum Gravit. 26(6), 065004 (2009)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  14. Gangopadhyay, S., Dutta, A., Faizal, M.: Constraints on the generalized uncertainty principle from black-hole thermodynamics. EPL 112(2), 20006 (2015)

    Article  ADS  Google Scholar 

  15. Amelino-Camelia, G., Arzano, M., Ling, Y., Mandanici, G.: Black-hole thermodynamics with modified dispersion relations and generalized uncertainty principles. Class. Quantum Gravit. 23(7), 2585 (2006)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. Ling, Y., Li, X., Zhang, H.: Thermodynamics of modified black holes from gravity’s rainbow. Mod. Phys. Lett. A 22(36), 2749–2756 (2007)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  17. Galán, P., Marugán, G.A.M.: Entropy and temperature of black holes in a gravity’s rainbow. Phys. Rev. D 74, 044035 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  18. Hendi, S.H., Faizal, M., Panah, B.E., Panahiyan, S.: Charged dilatonic black holes in gravity’s rainbow. Eur. Phys. J. C 76(5), 296 (2016)

    Article  ADS  Google Scholar 

  19. Ali, A.F.: Black hole remnant from gravity’s rainbow. Phys. Rev. D 89, 104040 (2014)

    Article  ADS  Google Scholar 

  20. Adler, Ronald J., Chen, Pisin, Santiago, David I.: The generalized uncertainty principle and black hole remnants. Gen. Relativ. Gravit. 33(12), 2101–2108 (2001)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  21. Ling, Y.: Rainbow universe. JCAP 2007(08), 017 (2007)

    Article  ADS  Google Scholar 

  22. Awad, A., Ali, A.F., Majumder, B.: Nonsingular rainbow universes. JCAP 2013(10), 052 (2013)

    Article  Google Scholar 

  23. Hendi, S.H., Momennia, M., Panah, B.E., Faizal, M.: Nonsingular universes in Gauss–Bonnet gravity’s rainbow. ApJ 827(2), 153 (2016)

    Article  ADS  Google Scholar 

  24. Majumder, B.: Singularity free rainbow universe. Int. J. Mod. Phys. D 22(12), 1342021 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  25. Olmo, G.J.: Palatini actions and quantum gravity phenomenology. JCAP 2011(10), 018 (2011)

    Article  Google Scholar 

  26. Ling, Y., Wu, Q.: The big bounce in rainbow universe. Phys. Lett. B 687(2), 103–109 (2010)

    Article  ADS  Google Scholar 

  27. Hendi, S.H., Faizal, M.: Black holes in Gauss–Bonnet gravity’s rainbow. Phys. Rev. D 92, 044027 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  28. Hendi, S.H., Panahiyan, S., Panah, B.E., Faizal, M., Momennia, M.: Critical behavior of charged black holes in Gauss–Bonnet gravity’s rainbow. Phys. Rev. D 94, 024028 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  29. Hendi, S.H., Panah, B.E., Panahiyan, S.: Topological charged black holes in massive gravity’s rainbow and their thermodynamical analysis through various approaches. Phys. Lett. B B769, 191–201 (2017)

    Article  ADS  MATH  Google Scholar 

  30. Hendi, S.H., Panahiyan, S., Upadhyay, S., Panah, B.E.: Charged BTZ black holes in the context of massive gravity’s rainbow. Phys. Rev. D 95, 084036 (2017)

    Article  ADS  Google Scholar 

  31. Hendi, S. H., Panah, B. E., Panahiyan, S., Momennial, M.: \({F(R)}\) gravity’s rainbow and its Einstein counterpart. Adv. High Energy Phys., 2016:9813582, (2016)

  32. Garattini, R.: Distorting general relativity: gravity’s rainbow and \(f({R})\) theories at work. JCAP 2013(06), 017 (2013)

    Article  Google Scholar 

  33. Garattini, R., Saridakis, E.N.: Gravity’s rainbow: a bridge towards Hořava–Lifshitz gravity. Eur. Phys. J. C 75(7), 343 (2015)

    Article  ADS  Google Scholar 

  34. Faraoni, V., Gunzig, E., Nardone, P.: Conformal transformations in classical gravitational theories and in cosmology. Fund. Cosmic Phys. 20, 121 (1999)

    ADS  Google Scholar 

  35. Dicke, R.H.: Mach’s principle and invariance under transformation of units. Phys. Rev. 125, 2163–2167 (1962)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  36. Dabrowski, M.P., Garecki, J., Blaschke, D.B.: Conformal transformations and conformal invariance in gravitation. Ann. der Phys. 18(1), 13–32 (2009)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  37. Hendi, S.H., Talezadeh, M.S.: Nonlinearly charged dilatonic black holes and their Brans–Dicke counterpart: energy dependent spacetime. Gen. Relativ. Gravit 49(1), 12 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  38. Magnano, G., Sokołowski, L.M.: Physical equivalence between nonlinear gravity theories and a general-relativistic self-gravitating scalar field. Phys. Rev. D 50, 5039–5059 (1994)

    Article  ADS  MathSciNet  Google Scholar 

  39. Kimberly, D., Magueijo, J., Medeiros, J.: Nonlinear relativity in position space. Phys. Rev. D 70, 084007 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  40. De Felice, A., Tsujikawa, S.: \(f({R})\) Theories. Living Rev. Rel. 13(1), 3 (2010)

    Article  MATH  Google Scholar 

  41. Capozziello, S., De Felice, A.: \(f({R})\) cosmology from Noether’s symmetry. JCAP 2008(08), 016 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  42. Sotiriou, T.P., Faraoni, V.: \(f({R})\) theories of gravity. Rev. Mod. Phys. 82, 451–497 (2010)

    Article  ADS  MATH  Google Scholar 

  43. Alexander, S., Magueijo, J.: Non-commutative geometry as a realization of varying speed of light cosmology. arXiv preprint hep-th/0104093 (2001)

  44. Amendola, L., Polarski, D., Tsujikawa, S.: Are \(f({R})\) dark energy models cosmologically viable? Phys. Rev. Lett. 98, 131302 (2007)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  45. Amendola, L., Gannouji, R., Polarski, D., Tsujikawa, S.: Conditions for the cosmological viability of \(f({R})\) dark energy models. Phys. Rev. D 75, 083504 (2007)

    Article  ADS  Google Scholar 

  46. Carroll, S.M., Duvvuri, V., Trodden, M., Turner, M.S.: Is cosmic speed-up due to new gravitational physics? Phys. Rev. D 70, 043528 (2004)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We would like to thank the National Natural Science Foundation of China (Grant No. 11571342) for supporting us on this work.

Author information

Authors and Affiliations

  1. Institute of Theoretical Physics, LanZhou University, Lanzhou, 730000, People’s Republic of China

    Miao He, Ping Li, Zi-Liang Wang, Jia-Cheng Ding & Jian-Bo Deng

Authors
  1. Miao He
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ping Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zi-Liang Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jia-Cheng Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Jian-Bo Deng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jian-Bo Deng.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

He, M., Li, P., Wang, ZL. et al. Conformal transformation route to gravity’s rainbow. Gen Relativ Gravit 50, 22 (2018). https://doi.org/10.1007/s10714-018-2339-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10714-018-2339-7

Keywords

Search

Navigation