On Newtonian singularities in higher derivative gravity models

  • Leonardo Modesto
  • Tibério de Paula Netto
  • Ilya L. Shapiro
Open Access
Regular Article - Theoretical Physics

Abstract

We consider the problem of Newtonian singularity in the wide class of higher derivative gravity models, including the ones which are renormalizable and super-renormalizable at the quantum level. The simplest version of the singularity-free theory has four derivatives and is pretty well-known. We argue that in all cases of local higher-derivative theories, when the poles of the propagator are real and simple, the singularities disappear due to the cancelation of contributions from scalar and tensor massive modes.

Keywords

Models of Quantum Gravity Classical Theories of Gravity 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    A.A. Starobinsky, A New Type of Isotropic Cosmological Models Without Singularity, Phys. Lett. B 91 (1980) 99 [INSPIRE].ADSCrossRefMATHGoogle Scholar
  2. [2]
    M.V. Fischetti, J.B. Hartle and B.L. Hu, Quantum Effects in the Early Universe. I. Influence of Trace Anomalies on Homogeneous, Isotropic, Classical Geometries, Phys. Rev. D 20 (1979) 1757 [INSPIRE].ADSMathSciNetGoogle Scholar
  3. [3]
    P.R. Anderson, Effects of quantum fields on singularities and particle horizons in the early universe, Phys. Rev. D 28 (1983) 271 [INSPIRE].ADSMathSciNetGoogle Scholar
  4. [4]
    P.R. Anderson, Effects of quantum fields on singularities and particle horizons in the early universe. II, Phys. Rev. D 29 (1984) 615 [INSPIRE].ADSGoogle Scholar
  5. [5]
    P.R. Anderson, Effects of Quantum Fields on Singularities and Particle Horizons in the Early Universe. III. The Conformally Coupled Massive Scalar Field, Phys. Rev. D 32 (1985) 1302 [INSPIRE].ADSGoogle Scholar
  6. [6]
    P.R. Anderson, Effects of Quantum Fields on Singularities and Particle Horizons in the Early Universe. IV. Initially Empty Universes, Phys. Rev. D 33 (1986) 1567 [INSPIRE].ADSGoogle Scholar
  7. [7]
    V.P. Frolov and G.A. Vilkovisky, Spherically Symmetric Collapse in Quantum Gravity, Phys. Lett. B 106 (1981) 307 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  8. [8]
    V.P. Frolov and I.L. Shapiro, Black Holes in Higher Dimensional Gravity Theory with Quadratic in Curvature Corrections, Phys. Rev. D 80 (2009) 044034 [arXiv:0907.1411] [INSPIRE].ADSGoogle Scholar
  9. [9]
    L. Modesto, Super-renormalizable Quantum Gravity, Phys. Rev. D 86 (2012) 044005 [arXiv:1107.2403] [INSPIRE].ADSGoogle Scholar
  10. [10]
    T. Biswas, A. Mazumdar and W. Siegel, Bouncing universes in string-inspired gravity, JCAP 03 (2006) 009 [hep-th/0508194] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  11. [11]
    T. Biswas, T. Koivisto and A. Mazumdar, Towards a resolution of the cosmological singularity in non-local higher derivative theories of gravity, JCAP 11 (2010) 008 [arXiv:1005.0590] [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    T. Biswas, E. Gerwick, T. Koivisto and A. Mazumdar, Towards singularity- and ghost-free theories of gravity, Phys. Rev. Lett. 108 (2012) 031101 [arXiv:1110.5249] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    P. Nicolini, A. Smailagic and E. Spallucci, Noncommutative geometry inspired Schwarzschild black hole, Phys. Lett. B 632 (2006) 547 [gr-qc/0510112] [INSPIRE].
  14. [14]
    L. Modesto, J.W. Moffat and P. Nicolini, Black holes in an ultraviolet complete quantum gravity, Phys. Lett. B 695 (2011) 397 [arXiv:1010.0680] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  15. [15]
    L. Modesto, Super-renormalizable Higher-Derivative Quantum Gravity, arXiv:1202.0008 [INSPIRE].
  16. [16]
    E.T. Tomboulis, Superrenormalizable gauge and gravitational theories, hep-th/9702146 [INSPIRE].
  17. [17]
    L. Modesto and L. Rachwal, Super-renormalizable and finite gravitational theories, Nucl. Phys. B 889 (2014) 228 [arXiv:1407.8036] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  18. [18]
    A.A. Tseytlin, On singularities of spherically symmetric backgrounds in string theory, Phys. Lett. B 363 (1995) 223 [hep-th/9509050] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  19. [19]
    W. Siegel, Stringy gravity at short distances, hep-th/0309093 [INSPIRE].
  20. [20]
    M. Asorey, J.L. Lopez and I.L. Shapiro, Some remarks on high derivative quantum gravity, Int. J. Mod. Phys. A 12 (1997) 5711 [hep-th/9610006] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  21. [21]
    E.V. Gorbar and I.L. Shapiro, Renormalization group and decoupling in curved space, JHEP 02 (2003) 021 [hep-ph/0210388] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  22. [22]
    E.V. Gorbar and I.L. Shapiro, Renormalization group and decoupling in curved space. 2. The standard model and beyond, JHEP 06 (2003) 004 [hep-ph/0303124] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  23. [23]
    K.S. Stelle, Renormalization of Higher Derivative Quantum Gravity, Phys. Rev. D 16 (1977) 953 [INSPIRE].ADSMathSciNetGoogle Scholar
  24. [24]
    K.S. Stelle, Classical Gravity with Higher Derivatives, Gen. Rel. Grav. 9 (1978) 353 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  25. [25]
    F. de O. Salles and I.L. Shapiro, Do we have unitary and (super)renormalizable quantum gravity below the Planck scale?, Phys. Rev. D 89 (2014) 084054 [arXiv:1401.4583] [INSPIRE].
  26. [26]
    I.L. Shapiro, A.M. Pelinson and F. de O. Salles, Gravitational Waves and Perspectives for Quantum Gravity, Mod. Phys. Lett. A 29 (2014) 1430034 [arXiv:1410.2581] [INSPIRE].
  27. [27]
    L. Modesto, Super-renormalizable Multidimensional Quantum Gravity, arXiv:1202.3151 [INSPIRE].
  28. [28]
    L. Modesto, Finite Quantum Gravity, arXiv:1305.6741 [INSPIRE].
  29. [29]
    T. Biswas, T. Koivisto and A. Mazumdar, Nonlocal theories of gravity: the flat space propagator, arXiv:1302.0532 [INSPIRE].
  30. [30]
    T. Biswas, A. Conroy, A.S. Koshelev and A. Mazumdar, Generalized ghost-free quadratic curvature gravity, Class. Quant. Grav. 31 (2014) 015022 [Erratum ibid. 31 (2014) 159501] [arXiv:1308.2319] [INSPIRE].
  31. [31]
    I.L. Buchbinder, S.D. Odintsov and I.L. Shapiro, Effective Action in Quantum Gravity, IOP Publishing, Bristol, U.K. (1992).Google Scholar
  32. [32]
    I. Quandt and H.-J. Schmidt, The Newtonian limit of fourth and higher order gravity, Astron. Nachr. 312 (1991) 97 [gr-qc/0109005] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  33. [33]
    S.W. Hawking, Whos Afraid Of (higher Derivative) Ghosts?, in Quantum Field Theory and Quantum Statistics 2 (1986) 129-139 [INSPIRE].
  34. [34]
    S.W. Hawking and T. Hertog, Living with ghosts, Phys. Rev. D 65 (2002) 103515 [hep-th/0107088] [INSPIRE].ADSMathSciNetGoogle Scholar
  35. [35]
    H. Lü, A. Perkins, C.N. Pope and K.S. Stelle, Black Holes in Higher-Derivative Gravity, arXiv:1502.01028 [INSPIRE].
  36. [36]
    B. Holdom, On the fate of singularities and horizons in higher derivative gravity, Phys. Rev. D 66 (2002) 084010 [hep-th/0206219] [INSPIRE].ADSMathSciNetGoogle Scholar
  37. [37]
    C. Bambi, D. Malafarina and L. Modesto, Terminating black holes in asymptotically free quantum gravity, Eur. Phys. J. C 74 (2014) 2767 [arXiv:1306.1668] [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    I.L. Shapiro, Counting ghosts in theghost-freenon-local gravity, Phys. Lett. B 744 (2015) 67 [arXiv:1502.00106] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar

Copyright information

© The Author(s) 2015

Authors and Affiliations

  • Leonardo Modesto
    • 1
  • Tibério de Paula Netto
    • 2
    • 3
  • Ilya L. Shapiro
    • 3
    • 4
    • 5
  1. 1.Department of Physics & Center for Field Theory and Particle PhysicsFudan UniversityShanghaiChina
  2. 2.Department of PhysicsUniversity of AlbertaEdmontonCanada
  3. 3.Departamento de Fisica — ICEUniversidade Federal de Juiz de ForaJuiz de ForaBrazil
  4. 4.Département de Physique Théorique and Center for Astroparticle PhysicsUniversité de GenèveGenéve 4Switzerland
  5. 5.Tomsk State Pedagogical University, Tomsk State UniversityTomskRussia

Personalised recommendations