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DOMOSCHOOL 2018: Einstein Equations: Physical and Mathematical Aspects of General Relativity pp 243–265Cite as

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

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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.

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References

  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. M. Alcubierre, The warp drive: hyper-fast travel within general relativity. Class. Quant. Grav. 11, L73-L77 (1994)

    Article  ADS  MathSciNet  Google Scholar 

  3. A. Bachelot, Global properties of the wave equation on non-globally hyperbolic manifolds. J. Math. Pures Appl. 81, 35–65 (2002)

    Article  MathSciNet  Google Scholar 

  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. J. Dietz, A. Dirmeier, M. Scherfner, Geometric analysis of Ori-type spacetimes, 24pp. (2012). arXiv:1201.1929 [gr-qc]

    Google Scholar 

  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)

    Article  ADS  MathSciNet  Google Scholar 

  7. H. Ellis, Ether flow through a drainhole: a particle model in general relativity. J. Math. Phys. 14, 104–118 (1973)

    Article  ADS  MathSciNet  Google Scholar 

  8. A.E. Everett, Warp drive and causality. Phys. Rev. D 53(12), 7365–7368 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  9. A.E. Everett, T.A. Roman, Superluminal subway: the Krasnikov tube. Phys. Rev. D 56(4), 2100–2108 (1997)

    Article  ADS  MathSciNet  Google Scholar 

  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. 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. 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)

    Article  ADS  MathSciNet  Google Scholar 

  13. V. Frolov, I. Novikov, Black Hole Physics. Basic Concepts and New Developments (Kluwer Academic Publisher, Dordrecht, 1998)

    Google Scholar 

  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)

    Article  ADS  MathSciNet  Google Scholar 

  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)

    Article  ADS  MathSciNet  Google Scholar 

  16. J.D.E. Grant, Cosmic strings and chronology protection. Phys. Rev. D 47(6), 2388–2394 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  17. S.W. Hawking, Chronology protection conjecture. Phys. Rev. D 46(2), 603–611 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  18. S.W. Hawking, G.F.R. Ellis, The Large Scale Structure of Space-Time (Cambridge University Press, Cambridge, 1975)

    MATH  Google Scholar 

  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)

    Article  ADS  MathSciNet  Google Scholar 

  20. S.V. Krasnikov, Hyperfast travel in general relativity. Phys. Rev. D 57(8), 4760–4766 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  21. S.V. Krasnikov, Time machines with the compactly determined Cauchy horizon. Phys. Rev. D 90(2), 024067 (8pp.) (2014)

    Google Scholar 

  22. S.V. Krasnikov, Back-in-Time and Faster-Than-Light Travel in General Relativity (Springer, Berlin, 2018)

    Book  Google Scholar 

  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. F.S.N. Lobo, Wormholes, Warp Drives and Energy Conditions (Springer, Berlin, 2017)

    Book  Google Scholar 

  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. P. Martín-Moruno1, M. Visser, Essential core of the Hawking–Ellis types. Class. Quant. Grav. 35, 125003 (12pp.) (2018)

    Google Scholar 

  27. C.W. Misner, The flatter regions of Newman, Unti, and Tamburino’s generalized Schwarzschild space. J. Math. Phys. 4(7), 924–937 (1963)

    Article  ADS  MathSciNet  Google Scholar 

  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. 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)

    Article  ADS  MathSciNet  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  31. E. Newman, L. Tamburino, T. Unti, Empty space generalization of the Schwarzschild metric. J. Math. Phys. 4(7), 915–923 (1963)

    Article  ADS  MathSciNet  Google Scholar 

  32. A. Ori, Must time-machine construction violate the weak energy condition? Phys. Rev. Lett. 71, 2517–2520 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  33. A. Ori, A class of time-machine solutions with a compact vacuum core. Phys. Rev. Lett. 95, 021101 (4pp.) (2005)

    Google Scholar 

  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. A. Ori, Y. Soen, Causality violation and the weak energy condition. Phys. Rev. D 49(8), 3990–3997 (1994)

    Article  ADS  MathSciNet  Google Scholar 

  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. Y. Soen, A. Ori, Improved time-machine model. Phys. Rev. D 54(8), 4858–4861 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  38. A.H. Taub, Empty space-times admitting a three parameter group of motions. Ann. Math. 53(3), 472–490 (1951)

    Article  ADS  MathSciNet  Google Scholar 

  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. 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. F.J. Tipler, Rotating cylinders and the possibility of global causality violation. Phys. Rev. D 9(8), 2203–2206 (1974)

    Article  ADS  MathSciNet  Google Scholar 

  42. B.K. Tippett, D. Tsang, Traversable acausal retrograde domains in spacetime. Class. Quantum Grav. 34, 095006 (12pp.) (2017)

    Google Scholar 

  43. A. Tomimatsu, H. Sato, New series of exact solutions for gravitational fields of spinning masses. Prog. Theor. Phys. 50(1) (1973), 95–110

    Article  ADS  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  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. R.M. Wald, General Relativity (The University of Chicago Press, Chicago, 1984)

    Book  Google Scholar 

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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.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università degli Studi di Milano, Milano, Italy

    Davide Fermi

  2. Istituto Nazionale di Fisica Nucleare, Sezione di Milano, Italy

    Davide Fermi

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  1. Davide Fermi
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Correspondence to Davide Fermi .

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Editors and Affiliations

  1. Department of Science and High Technology, University Insubrien, Como, Italy

    Sergio Cacciatori

  2. Mathematisches Institut, Humboldt-Universität zu Berlin, Berlin, Germany

    Batu Güneysu

  3. Department of Science and High Technology, University Insubrien, Como, Italy

    Stefano Pigola

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Fermi, D. (2019). Some Remarks on a New Exotic Spacetime for Time Travel by Free Fall. In: Cacciatori, S., Güneysu, B., Pigola, S. (eds) Einstein Equations: Physical and Mathematical Aspects of General Relativity. DOMOSCHOOL 2018. Tutorials, Schools, and Workshops in the Mathematical Sciences . Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-18061-4_8

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