Abstract
We analyze what we believe to be all known homogeneous rotating \(\varLambda \)-dust cosmologies, to see if they contain closed timelike loops (CTLs). We investigate only these exact GR solutions because they appear to most closely resemble our own universe (apart from rotation and expansion). These solutions are all somewhat similar to the Gödel solution, which is known to contain CTLs. Of these solutions, it turns out that exactly those with \(\varLambda <0\) possess CTLs. The paper also analyzes the solutions to see if they satisfy the four “Energy Conditions” (Weak, Null, Strong, Dominant), and shows that all four are satisfied—but only by the families containing CTLs! It is amusing to note that our current universe violates the Strong Energy Condition.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Nahin, P.: Time Machines: Time Travel in Physics, Metaphysics, and Science Fiction. Springer, New York (1999)
Tipler, F.: Rotating cylinders and the possibility of causality violation. Phys. Rev. 9(8), 2203–2206 (1974)
van Stockum, W.: Proc. R. Soc. Edinb. 57, 135 (1937)
Lánczos, K.: Über eine stationäre Kosmologie im Sinne der Einsteinschen Gravitationstheorie. Z. Angew. Phys. 21, 73–110 (1924)
Gödel, K.: An example of a new type of cosmological solutions of Einstein’s field equations of gravitation. Rev. Mod. Phys. 21, 447–450 (1949)
Rosquist, K.: Global rotation. Gen. Relativ. Gravit. 12(8), 649–664 (1980)
Hawking, S., Ellis, G.: The Large Scale Structure of Space-Time. Cambridge University Press, Cambridge (1973)
Carter, B.: Global structure of the Kerr family of gravitational fields. Phys. Rev. 174(5), 1559–1571 (1968)
Stephani, H., Kramer, D., et al.: Exact Solutions of Einstein’s Field Equations (Second Edition). Cambridge Monographs on Mathematical Physics, Cambridge (2003)
Korotkii, V., Obukhov, Y.: Rotating and expanding cosmology in ECSK theory. Astrophys. Space Sci. 198(1), 1–12 (1992)
Assad, M., Soares, J.: Anisotropic bianchi types VIII and IX locally rotationally symmetric cosmologies. Phys. Rev. D 28, 1858–1865 (1983)
Krasiński, A.: Rotating dust solutions of Einstein’s equations with 3-dimensional symmetry groups. I. Two Killing fields spanned on \(u^\alpha \) and \(w^\alpha \). J. Math. Phys. 39, 380 (1998)
Krasiński, A.: Rotating dust solutions of Einstein’s equations with 3-dimensional symmetry groups, Part 2: One killing field spanned on \(u^\alpha \) and \(w^\alpha \). J. Math. Phys. 39, 401 (1998)
Krasiński, A.: Rotating dust solutions of Einstein’s equations with 3-dimensional symmetry groups, Part 3: All killing fields linearly independent of \(u^\alpha \) and \(w^\alpha \). J. Math. Phys. 39, 2148 (1998)
Krasiński, A.: Rotating Bianchi type V dust models generalizing the k = -1 Friedmann model. J. Math. Phys. 42, 355 (2001)
Krasiński, A.: Friedmann limits of rotating hypersurface-homogeneous dust models. J. Math. Phys. 42, 3628 (2001)
Ozsváth, I.: New homogeneous solutions of Einstein’s field equations with incoherent matter, Akad. Wiss. Lit. Mainz, Abh. Math.-Nat. K1. 1 (1965)
Ozsváth, I., Schücking, E.: The finite rotating universe. Ann. Phys. 55, 166 (1969)
Ozsváth, I.: Dust-filled universes of Class II and Class III. J. Math. Phys. 11(9), 2871–2882 (1970)
Obukhov, Y., Chrobok, T., Scherfner, M.: Shear-free rotating inflation. Phys. Rev. D 66, 043518 (2002)
Raychaudhuri, A., Thakurta, S.: Homogeneous space-times of the Gödel type. Phys. Rev. D 22, 802 (1980)
Maitra, S.C.: Stationary dust-filled cosmological solution with \(\Lambda =0\) and without closed timelike lines. J. Math. Phys. 7, 1025 (1966)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Lindsay, D.S. Closed timelike loops in homogeneous rotating \(\varLambda \)-dust cosmologies. Gen Relativ Gravit 47, 83 (2015). https://doi.org/10.1007/s10714-015-1919-z
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10714-015-1919-z