Table of Contents
Journal of Gravity
Volume 2016 (2016), Article ID 4597905, 11 pages
http://dx.doi.org/10.1155/2016/4597905
Research Article

Non-Perfect-Fluid Space-Times in Thermodynamic Equilibrium and Generalized Friedmann Equations

Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany

Received 9 June 2016; Revised 29 August 2016; Accepted 13 October 2016

Academic Editor: Sergei D. Odintsov

Copyright © 2016 Konrad Schatz et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. G. F. R. Ellis, “Relativistic cosmology,” in Proceedings of the International School of Physics “Enrico Fermi”, Course 47: General Relativity and Cosmology, R. K. Sachs, Ed., pp. 104–182, Academic Press, New York, NY, USA, 1971. View at Google Scholar
  2. V. A. Korotky and Y. N. Obukhov, “Bianchi-II rotating world,” Astrophysics and Space Science, vol. 260, no. 4, pp. 425–439, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  3. Y. N. Obukhov, “Observations in rotating cosmologies. Gauge theories of fundamental interactions,” in Proceedings of the 32nd Semester in the Stefan Banach International Mathematical Center, M. Pawlowski and R. Raczka, Eds., World Scientific, Warsaw, Poland, 1990.
  4. Y. N. Obukhov, “On physical foundations and observational effects of cosmic rotation,” in Colloquium on Cosmic Rotation, M. Scherfner, Ed., Wissenschaft und Technik, 2000. View at Google Scholar
  5. Y. N. Obukhov, T. Chrobok, and M. Scherfner, “Shear-free rotating inflation,” Physical Review D, vol. 66, no. 4, Article ID 043518, 2002. View at Publisher · View at Google Scholar · View at Scopus
  6. S. Capozziello, V. F. Cardone, E. Elizalde, S. Nojiri, and S. D. Odintsov, “Observational constraints on dark energy with generalized equations of state,” Physical Review D—Particles, Fields, Gravitation and Cosmology, vol. 73, no. 4, Article ID 043512, 2006. View at Publisher · View at Google Scholar · View at Scopus
  7. R. Myrzakulov and L. Sebastiani, “Bounce solutions in viscous fluid cosmology,” Astrophysics and Space Science, vol. 352, no. 1, pp. 281–288, 2014. View at Publisher · View at Google Scholar · View at Scopus
  8. S. Nojiri and S. D. Odintsov, “Final state and thermodynamics of a dark energy universe,” Physical Review D, vol. 70, no. 10, Article ID 103522, 2004. View at Publisher · View at Google Scholar · View at Scopus
  9. S. Nojiri and S. D. Odintsov, “Inhomogeneous equation of state of the universe: phantom era, future singularity, and crossing the phantom barrier,” Physical Review D, vol. 72, Article ID 023003, 2005. View at Google Scholar
  10. R. Treciokas and G. F. R. Ellis, “Isotropic solutions of the Einstein-Boltzmann equations,” Communications in Mathematical Physics, vol. 23, no. 1, pp. 1–22, 1971. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. T. Chrobok and H.-H. V. Borzeszkowski, “Thermodynamic equilibrium and rotating space-time,” in Gödel-Type Spacetimes: History and New Developments, M. Scherfner and M. Plaue, Eds., pp. 7–22, Kurt Gödel Society, Collegium Logicum X, 2010. View at Google Scholar
  12. J. Ehlers, P. Geren, and R. K. Sachs, “Isotropic solutions of the Einstein-Liouville equations,” Journal of Mathematical Physics, vol. 9, no. 9, pp. 1344–1349, 1968. View at Publisher · View at Google Scholar · View at Scopus
  13. K. L. Duggal, “Relativistic fluids with shear and timelike conformal collineations,” Journal of Mathematical Physics, vol. 28, no. 11, pp. 2700–2704, 1987. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. D. R. Oliver Jr. and W. R. Davis, “On certain timelike symmetry properties and the evolution of matter field space-times that admit them,” General Relativity and Gravitation, vol. 8, no. 11, pp. 905–914, 1977. View at Google Scholar · View at MathSciNet
  15. W. Hasse and V. Perlick, “Geometrical and kinematical characterization of parallax-free world models,” Journal of Mathematical Physics, vol. 29, no. 9, pp. 2064–2068, 1988. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. A. A. Coley, “Fluid spacetimes admitting a conformal Killing vector parallel to the velocity vector,” Classical and Quantum Gravity, vol. 8, no. 5, pp. 955–968, 1991. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. R. K. Barrett and C. A. Clarkson, “Undermining the cosmological principle: almost isotropic observations in inhomogeneous cosmologies,” Classical and Quantum Gravity, vol. 17, no. 24, pp. 5047–5078, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. C. A. Clarkson and R. K. Barrett, “Does the isotropy of the CMB imply a homogeneous universe? Some generalized EGS theorems,” Classical and Quantum Gravity, vol. 16, no. 12, pp. 3781–3794, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. C. A. Clarkson, A. A. Coley, E. S. D. O'Neill, R. A. Sussman, and R. K. Barrett, “Inhomogeneous cosmologies, the copernican principle and the cosmic microwave background: more on the EGS theorem,” General Relativity and Gravitation, vol. 35, no. 6, pp. 969–990, 2003. View at Publisher · View at Google Scholar · View at Scopus
  20. H. Stephani, D. Kramer, M. MacCallum, C. Hoenselaers, and E. Herlt, Exact Solutions of Einstein's Field Equations, Cambridge Monographs on Mathematical Physics, Cambridge University Press, 2nd edition, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  21. T. Chrobok and H.-H. v. Borzeszkowski, “Thermodynamical equilibrium and spacetime geometry,” General Relativity and Gravitation, vol. 38, no. 3, pp. 397–415, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. C. Eckart, “The thermodynamics of irreversible processes. III. Relativistic theory of the simple fluid,” APS Journals Archive, vol. 58, no. 10, p. 919, 1940. View at Publisher · View at Google Scholar
  23. W. Israel, “Covariant fluid mechanics and thermodynamics: an introduction,” in Relativistic Fluid Dynamics, A. Anile and Y. Choquet-Bruhat, Eds., vol. 1385 of Lecture Notes in Mathematics, pp. 152–210, Springer, Berlin, Germany, 1989. View at Publisher · View at Google Scholar · View at MathSciNet
  24. G. Neugebauer, Relativistische Thermodynamik, Akademie, 1980. View at MathSciNet
  25. S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, John Wiley & Sons, New York, NY, USA, 1972.
  26. H.-H. Borzeszkowski, T. Chrobok, and W. Muschik, “Thermodynamical equilibrium and space-time geometry—a survey,” Communications in Applied and Industrial Mathematics, vol. 1, no. 2, pp. 206–215, 2010. View at Google Scholar · View at MathSciNet
  27. G. O. Schellstede, H.-H. von Borzeszkowski, T. Chrobok, and W. Muschik, “The relation between relativistic and non-relativistic continuum thermodynamics,” General Relativity and Gravitation, vol. 46, article 1640, 2014. View at Publisher · View at Google Scholar · View at Scopus
  28. H. Stephani, General Relativity, Cambridge University Press, 1982. View at MathSciNet
  29. M. L. Bedran and M. O. Calvao, “Reversibility and spacetime symmetries,” Classical and Quantum Gravity, vol. 10, no. 4, pp. 767–771, 1993. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  30. J. Triginer and D. Pavón, “On the thermodynamics of tilted and collisionless gases in Friedmann-Robertson-Walker spacetimes,” Classical and Quantum Gravity, vol. 12, no. 1, pp. 199–207, 1995. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  31. W. Zimdahl and A. B. Balakin, “Thermodynamic equilibrium in the expanding universe,” General Relativity and Gravitation, vol. 31, no. 9, pp. 1395–1405, 1999. View at Publisher · View at Google Scholar · View at Scopus
  32. W. Zimdahl and A. B. Balakin, “Cosmological thermodynamics and deflationary gas universe,” Physical Review D, vol. 63, no. 2, Article ID 023507, 2000. View at Publisher · View at Google Scholar
  33. W. Zimdahl, D. J. Schwarz, A. B. Balakin, and D. Pavón, “Cosmic antifriction and accelerated expansion,” Physical Review D, vol. 64, no. 6, Article ID 063501, 2001. View at Publisher · View at Google Scholar
  34. W. Zimdahl, D. J. Schwarz, A. B. Balakin, and D. Pavon, “Conformal symmetry and cosmological entropy production,” Entropy, vol. 4, no. 3, pp. 49–127, 2002. View at Publisher · View at Google Scholar
  35. A. R. King and G. F. Ellis, “Tilted homogeneous cosmological models,” Communications in Mathematical Physics, vol. 31, pp. 209–242, 1973. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  36. S. Chandrasekhar, The Mathematical Theory of Black Holes, Clarendon Pr. u.a, Oxford, UK, 1983.
  37. A. A. Coley and D. J. McManus, “On spacetimes admitting shear-free, irrotational, geodesic time-like congruences,” Classical and Quantum Gravity, vol. 11, no. 5, pp. 1261–1282, 1994. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  38. V. Perlick, “Gravitational lensing from a spacetime perspective,” Living Reviews in Relativity, vol. 7, article 9, 2004. View at Publisher · View at Google Scholar · View at Scopus
  39. E. Rebhan, Theoretische Physik: Relativitätstheorie und Kosmologie, Springer Spektrum, Heidelberg, Germany, 2012. View at Publisher · View at Google Scholar
  40. T. Chrobok, Scherungsfreie fluide in der allgemeinen relativitätstheorie [Ph.D. thesis], TU, Berlin, Germany, 2004.
  41. S. Harris, “Conformally stationary spacetimes,” Classical and Quantum Gravity, vol. 9, no. 7, pp. 1823–1827, 1992. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  42. L. Herrera, A. Di Prisco, and J. Ibáñez, “Reversible dissipative processes, conformal motions and Landau damping,” Physics Letters A, vol. 376, no. 8-9, pp. 899–900, 2012. View at Publisher · View at Google Scholar · View at Scopus
  43. I. Müller and T. Ruggeri, Extended Thermodynamics, vol. 37, Springer, New York, NY, USA, 1993. View at Publisher · View at Google Scholar · View at MathSciNet
  44. A. Kashlinsky, F. Atrio-Barandela, and H. Ebeling, “Measuring bulk motion of X-ray clusters via the kinematic Sunyaev-Zeldovich effect: summarizing the ‘dark flow’ evidence and its implications,” https://arxiv.org/abs/1202.0717.
  45. R. M. Wald, General Relativity, University of Chicago Press, Chicago, Ill, USA, 1984. View at Publisher · View at Google Scholar · View at MathSciNet