Advertisement

Some Remarks on a New Exotic Spacetime for Time Travel by Free Fall

  • Davide FermiEmail author
Chapter
Part of the Tutorials, Schools, and Workshops in the Mathematical Sciences book series (TSWMS)

Abstract

This work is essentially a review of a new spacetime model with closed causal curves, recently presented in another paper. The spacetime at issue is topologically trivial, free of curvature singularities, and even time and space orientable. Besides summarizing previous results on causal geodesics, tidal accelerations, and violations of the energy conditions, here redshift/blueshift effects and the Hawking–Ellis classification of the stress–energy tensor are examined.

Keywords

General relativity Closed causal curves Time machines Energy conditions Hawking–Ellis classification 

Mathematics Subject Classification (2000)

Primary 83C99; Secondary 83-06 

Notes

Acknowledgements

I wish to thank Livio Pizzocchero for valuable comments and suggestions. This work was supported by: INdAM, Gruppo Nazionale per la Fisica Matematica; “Progetto Giovani GNFM 2017 - Dinamica quasi classica per il modello di polarone” fostered by GNFM-INdAM; INFN, Istituto Nazionale di Fisica Nucleare.

References

  1. 1.
    F. Ahmed, A type N radiation field solution with Λ < 0 in a curved space-time and closed time-like curves. Eur. Phys. J. C 78, 385 (6pp.) (2018)Google Scholar
  2. 2.
    M. Alcubierre, The warp drive: hyper-fast travel within general relativity. Class. Quant. Grav. 11, L73-L77 (1994)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    A. Bachelot, Global properties of the wave equation on non-globally hyperbolic manifolds. J. Math. Pures Appl. 81, 35–65 (2002)MathSciNetCrossRefGoogle Scholar
  4. 4.
    S. Deser, R. Jackiw, G. ’t Hooft, Physical cosmic strings do not generate closed timelike curves. Phys. Rev. Lett. 68(3), 267–269 (1992)Google Scholar
  5. 5.
    J. Dietz, A. Dirmeier, M. Scherfner, Geometric analysis of Ori-type spacetimes, 24pp. (2012). arXiv:1201.1929 [gr-qc]Google Scholar
  6. 6.
    F. Echeverria, G. Klinkhammer, K.S. Thorne, Billiard balls in wormhole spacetimes with closed timelike curves: classical theory. Phys. Rev. D 44(4), 1077–1099 (1991)ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    H. Ellis, Ether flow through a drainhole: a particle model in general relativity. J. Math. Phys. 14, 104–118 (1973)ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    A.E. Everett, Warp drive and causality. Phys. Rev. D 53(12), 7365–7368 (1996)ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    A.E. Everett, T.A. Roman, Superluminal subway: the Krasnikov tube. Phys. Rev. D 56(4), 2100–2108 (1997)ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    D. Fermi, L. Pizzocchero, A time machine for free fall into the past. Class. Quant. Grav. 35(16), 165003 (42pp.) (2018)Google Scholar
  11. 11.
    J.L. Friedman, The Cauchy problem on spacetimes that are not globally hyperbolic, in The Einstein Equations and the Large Scale Behavior of Gravitational Fields, ed. by P.T. Chrusciel, H. Friedrich (Springer/Birkhäuser, Basel, 2004)Google Scholar
  12. 12.
    J. Friedman, M.S. Morris, I.D. Novikov, F. Echeverria, G. Klinkhammer, K.S. Thorne, U. Yurtsever, Cauchy problem in spacetimes with closed timelike curves. Phys. Rev. D 42(6), 1915–1930 (1990)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    V. Frolov, I. Novikov, Black Hole Physics. Basic Concepts and New Developments (Kluwer Academic Publisher, Dordrecht, 1998)Google Scholar
  14. 14.
    K. Gödel, An example of a new type of cosmological solutions of Einstein’s field equations of gravitation. Rev. Mod. Phys. 21(3), 447–450 (1949)ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    J.R. Gott III, Closed timelike curves produced by pairs of moving cosmic strings: exact solutions. Phys. Rev. Lett. 66(9), 1126–1129 (1991)ADSMathSciNetCrossRefGoogle Scholar
  16. 16.
    J.D.E. Grant, Cosmic strings and chronology protection. Phys. Rev. D 47(6), 2388–2394 (1993)ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    S.W. Hawking, Chronology protection conjecture. Phys. Rev. D 46(2), 603–611 (1992)ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    S.W. Hawking, G.F.R. Ellis, The Large Scale Structure of Space-Time (Cambridge University Press, Cambridge, 1975)zbMATHGoogle Scholar
  19. 19.
    R.P. Kerr, Gravitational field of a spinning mass as an example of algebraically special metrics. Phys. Rev. Lett. 11(5), 237–238 (1963)ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    S.V. Krasnikov, Hyperfast travel in general relativity. Phys. Rev. D 57(8), 4760–4766 (1998)ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    S.V. Krasnikov, Time machines with the compactly determined Cauchy horizon. Phys. Rev. D 90(2), 024067 (8pp.) (2014)Google Scholar
  22. 22.
    S.V. Krasnikov, Back-in-Time and Faster-Than-Light Travel in General Relativity (Springer, Berlin, 2018)CrossRefGoogle Scholar
  23. 23.
    F.S.N. Lobo, Closed timelike curves and causality violation, in Classical and Quantum Gravity: Theory, Analysis and Applications, ed. by V.R. Frignanni (Nova Science Publishers, New York, 2008)Google Scholar
  24. 24.
    F.S.N. Lobo, Wormholes, Warp Drives and Energy Conditions (Springer, Berlin, 2017)CrossRefGoogle Scholar
  25. 25.
    C. Mallary, G. Khanna, R.H. Price, Closed timelike curves and ‘effective’ superluminal travel with naked line singularities. Class. Quant. Grav. 35, 175020 (18pp.) (2018)Google Scholar
  26. 26.
    P. Martín-Moruno1, M. Visser, Essential core of the Hawking–Ellis types. Class. Quant. Grav. 35, 125003 (12pp.) (2018)Google Scholar
  27. 27.
    C.W. Misner, The flatter regions of Newman, Unti, and Tamburino’s generalized Schwarzschild space. J. Math. Phys. 4(7), 924–937 (1963)ADSMathSciNetCrossRefGoogle Scholar
  28. 28.
    C.W. Misner, Taub-NUT space as a counterexample to almost anything, in Relativity Theory and Astrophysics, ed. by J. Ehlers. Relativity and Cosmology, vol. 1 (AMS, Providence, 1967)Google Scholar
  29. 29.
    M.S. Morris, K.S. Thorne, Wormholes in spacetime and their use for interstellar travel: a tool for teaching general relativity. Am. J. Phys. 56(5), 395–412 (1988)ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    M.S. Morris, K.S. Thorne, U. Yurtsever, Wormholes, time machines, and the weak energy condition. Phys. Rev. Lett. 61(13), 1446–1449 (1988)ADSCrossRefGoogle Scholar
  31. 31.
    E. Newman, L. Tamburino, T. Unti, Empty space generalization of the Schwarzschild metric. J. Math. Phys. 4(7), 915–923 (1963)ADSMathSciNetCrossRefGoogle Scholar
  32. 32.
    A. Ori, Must time-machine construction violate the weak energy condition? Phys. Rev. Lett. 71, 2517–2520 (1993)ADSMathSciNetCrossRefGoogle Scholar
  33. 33.
    A. Ori, A class of time-machine solutions with a compact vacuum core. Phys. Rev. Lett. 95, 021101 (4pp.) (2005)Google Scholar
  34. 34.
    A. Ori, Formation of closed timelike curves in a composite vacuum/dust asymptotically flat spacetime. Phys. Rev. D 76(4), 044002 (14pp.) (2007)Google Scholar
  35. 35.
    A. Ori, Y. Soen, Causality violation and the weak energy condition. Phys. Rev. D 49(8), 3990–3997 (1994)ADSMathSciNetCrossRefGoogle Scholar
  36. 36.
    D. Sarma, M. Patgiri, F.U. Ahmed, Pure radiation metric with stable closed timelike curves. Gen. Relativ. Gravit. 46, 1633 (9pp.) (2014)Google Scholar
  37. 37.
    Y. Soen, A. Ori, Improved time-machine model. Phys. Rev. D 54(8), 4858–4861 (1996)ADSMathSciNetCrossRefGoogle Scholar
  38. 38.
    A.H. Taub, Empty space-times admitting a three parameter group of motions. Ann. Math. 53(3), 472–490 (1951)ADSMathSciNetCrossRefGoogle Scholar
  39. 39.
    K.S. Thorne, Closed timelike curves, in General Relativity and Gravitation, ed. by R.J. Gleiser, C.N. Kozameh, O.M. Moreschi, 1992. Proceedings of the 13th International Conference on General Relativity and Gravitation (Institute of Physics Publishing, Bristol, 1993)Google Scholar
  40. 40.
    K.S. Thorne, Misner space as a counterexample to almost any pathology, in Directions in General Relativity, ed. by B.L. Hu, M.P. Ryan Jr., C.V. Vishveshwara. Proceedings of the 1993 International Symposium, Maryland, vol. 1. Papers in Honor of Charles Misner (Cambridge University Press, Cambridge, 1993)Google Scholar
  41. 41.
    F.J. Tipler, Rotating cylinders and the possibility of global causality violation. Phys. Rev. D 9(8), 2203–2206 (1974)ADSMathSciNetCrossRefGoogle Scholar
  42. 42.
    B.K. Tippett, D. Tsang, Traversable acausal retrograde domains in spacetime. Class. Quantum Grav. 34, 095006 (12pp.) (2017)Google Scholar
  43. 43.
    A. Tomimatsu, H. Sato, New series of exact solutions for gravitational fields of spinning masses. Prog. Theor. Phys. 50(1) (1973), 95–110ADSMathSciNetCrossRefGoogle Scholar
  44. 44.
    W.J. van Stockum, The gravitational field of a distribution of particles rotating about an axis of symmetry. Proc. Royal Soc. Edinburgh 57, 135–154 (1938)CrossRefGoogle Scholar
  45. 45.
    M. Visser, The quantum physics of chronology protection, in Workshop on Conference on the Future of Theoretical Physics and Cosmology in Honor of Steven Hawking’s 60th Birthday. Proceedings, ed. by G.W. Gibbons, E.P.S. Shellard, S.J. Rankin (Cambridge University Press, Cambridge, 2002)Google Scholar
  46. 46.
    R.M. Wald, General Relativity (The University of Chicago Press, Chicago, 1984)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità degli Studi di MilanoMilanoItaly
  2. 2.Istituto Nazionale di Fisica NucleareSezione di MilanoItaly

Personalised recommendations