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Semiclassical energy conditions for quantum vacuum states

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Abstract

We present and develop several nonlinear energy conditions suitable for use in the semiclassical regime. In particular, we consider the recently formulated “flux energy condition” (FEC), and the novel “trace-of-square” (TOSEC) and “determinant” (DETEC) energy conditions. As we shall show, these nonlinear energy conditions behave much better than the classical linear energy conditions in the presence of semiclassical quantum effects. Moreover, whereas the quantum extensions of these nonlinear energy conditions seem to be quite widely satisfied as one enters the quantum realm, at least for quantum vacuum states, analogous quantum extensions are generally not useful for the linear classical energy conditions.

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References

  1. M. Visser, Lorentzian wormholes: from Einstein to Hawking, AIP Press, Woodbury U.S.A. (1995) [INSPIRE].

    Google Scholar 

  2. C. Barceló and M. Visser, Twilight for the energy conditions?, Int. J. Mod. Phys. D 11 (2002) 1553 [gr-qc/0205066] [INSPIRE].

    Article  ADS  Google Scholar 

  3. M. Visser, Energy conditions in the epoch of galaxy formation, Science 276 (1997) 88 [INSPIRE].

    Article  ADS  Google Scholar 

  4. M. Visser, General relativistic energy conditions: the Hubble expansion in the epoch of galaxy formation, Phys. Rev. D 56 (1997) 7578 [gr-qc/9705070] [INSPIRE].

    ADS  Google Scholar 

  5. M. Visser, Energy conditions and galaxy formation, gr-qc/9710010 [INSPIRE].

  6. H. Epstein, V. Glaser and A. Jaffe, Nonpositivity of energy density in quantized field theories, Nuovo Cim. 36 (1965) 1016 [INSPIRE].

    Article  MathSciNet  Google Scholar 

  7. M. Visser, Scale anomalies imply violation of the averaged null energy condition, Phys. Lett. B 349 (1995) 443 [gr-qc/9409043] [INSPIRE].

    Article  ADS  Google Scholar 

  8. M. Visser, Gravitational vacuum polarization. 1: Energy conditions in the Hartle-Hawking vacuum, Phys. Rev. D 54 (1996) 5103 [gr-qc/9604007] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  9. M. Visser, Gravitational vacuum polarization. 2: Energy conditions in the Boulware vacuum, Phys. Rev. D 54 (1996) 5116 [gr-qc/9604008] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  10. M. Visser, Gravitational vacuum polarization. 3: Energy conditions in the (1+1) Schwarzschild space-time, Phys. Rev. D 54 (1996) 5123 [gr-qc/9604009] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  11. M. Visser, Gravitational vacuum polarization. 4: Energy conditions in the Unruh vacuum, Phys. Rev. D 56 (1997) 936 [gr-qc/9703001] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  12. M. Visser, Gravitational vacuum polarization, gr-qc/9710034 [INSPIRE].

  13. E.E. Flanagan and R.M. Wald, Does back reaction enforce the averaged null energy condition in semiclassical gravity?, Phys. Rev. D 54 (1996) 6233 [gr-qc/9602052] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  14. C.J. Fewster and T.A. Roman, Null energy conditions in quantum field theory, Phys. Rev. D 67 (2003) 044003 [Erratum ibid. D 80 (2009) 069903] [gr-qc/0209036] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  15. C.J. Fewster, K.D. Olum and M.J. Pfenning, Averaged null energy condition in spacetimes with boundaries, Phys. Rev. D 75 (2007) 025007 [gr-qc/0609007] [INSPIRE].

    ADS  Google Scholar 

  16. L.H. Ford, A.D. Helfer and T.A. Roman, Spatially averaged quantum inequalities do not exist in four-dimensional space-time, Phys. Rev. D 66 (2002) 124012 [gr-qc/0208045] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  17. L.H. Ford, Constraints on negative energy fluxes, Phys. Rev. D 43 (1991) 3972 [INSPIRE].

    ADS  Google Scholar 

  18. L.H. Ford and T.A. Roman, Averaged energy conditions and quantum inequalities, Phys. Rev. D 51 (1995) 4277 [gr-qc/9410043] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  19. L.H. Ford and T.A. Roman, Quantum field theory constrains traversable wormhole geometries, Phys. Rev. D 53 (1996) 5496 [gr-qc/9510071] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  20. L.H. Ford and T.A. Roman, Motion of inertial observers through negative energy, Phys. Rev. D 48 (1993) 776 [gr-qc/9303038] [INSPIRE].

    ADS  Google Scholar 

  21. L.H. Ford and T.A. Roman, Restrictions on negative energy density in flat space-time, Phys. Rev. D 55 (1997) 2082 [gr-qc/9607003] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  22. L.H. Ford, M.J. Pfenning and T.A. Roman, Quantum inequalities and singular negative energy densities, Phys. Rev. D 57 (1998) 4839 [gr-qc/9711030] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  23. A. Borde, L.H. Ford and T.A. Roman, Constraints on spatial distributions of negative energy, Phys. Rev. D 65 (2002) 084002 [gr-qc/0109061] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  24. C.J. Fewster and L.W. Osterbrink, Quantum energy inequalities for the non-minimally coupled scalar field, J. Phys. A 41 (2008) 025402 [arXiv:0708.2450] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  25. C.J. Fewster, Quantum energy inequalities in two dimensions, Phys. Rev. D 70 (2004) 127501 [gr-qc/0411114] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  26. E.E. Flanagan, Quantum inequalities in two-dimensional curved space-times, Phys. Rev. D 66 (2002) 104007 [gr-qc/0208066] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  27. E.E. Flanagan, Quantum inequalities in two-dimensional Minkowski space-time, Phys. Rev. D 56 (1997) 4922 [gr-qc/9706006] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  28. C.J. Fewster and S.P. Eveson, Bounds on negative energy densities in flat space-time, Phys. Rev. D 58 (1998) 084010 [gr-qc/9805024] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  29. L.H. Ford and T.A. Roman, The quantum interest conjecture, Phys. Rev. D 60 (1999) 104018 [gr-qc/9901074] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  30. C.J. Fewster and E. Teo, Quantum inequalities andquantum interestas eigenvalue problems, Phys. Rev. D 61 (2000) 084012 [gr-qc/9908073] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  31. C.J. Fewster, A general worldline quantum inequality, Class. Quant. Grav. 17 (2000) 1897 [gr-qc/9910060] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  32. E. Teo and K.F. Wong, Quantum interest in two-dimensions, Phys. Rev. D 66 (2002) 064007 [gr-qc/0206066] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  33. C.J. Fewster and C.J. Smith, Absolute quantum energy inequalities in curved spacetime, Ann. Henri Poincaré 9 (2008) 425 [gr-qc/0702056] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  34. G. Abreu and M. Visser, Quantum interest in (3+1) dimensional Minkowski space, Phys. Rev. D 79 (2009) 065004 [arXiv:0808.1931] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  35. G. Abreu and M. Visser, The quantum interest conjecture in (3+1)-dimensional Minkowski space, arXiv:1001.1180 [INSPIRE].

  36. G. Abreu, C. Barceló and M. Visser, Entropy bounds in terms of the w parameter, JHEP 12 (2011) 092 [arXiv:1109.2710] [INSPIRE].

    Article  ADS  Google Scholar 

  37. P. Martín-Moruno and M. Visser, Classical and quantum flux energy conditions, arXiv:1305.1993 [INSPIRE].

  38. S.W. Hawking and G.F.R. Ellis, The large scale structure of space-time, Cambridge University Press, Cambridge U.K. (1973) [INSPIRE].

    Book  MATH  Google Scholar 

  39. D.N. Page, Thermal stress tensors in static Einstein spaces, Phys. Rev. D 25 (1982) 1499 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  40. M.R. Brown and A.C. Ottewill, Effective actions and conformal transformations, Phys. Rev. D 31 (1985) 2514 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  41. C.J. Fewster, L.H. Ford and and T.A. Roman, private communication.

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Correspondence to Prado Martín-Moruno.

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ArXiv ePrint: 1306.2076

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Martín-Moruno, P., Visser, M. Semiclassical energy conditions for quantum vacuum states. J. High Energ. Phys. 2013, 50 (2013). https://doi.org/10.1007/JHEP09(2013)050

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