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2011 | 9 | 4 | 1100-1105

Article title

Flowing liquid crystal simulating the Schwarzschild metric


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We show how to simulate the equatorial section of the Schwarzschild metric through a flowing liquid crystal in its nematic phase. Inside a liquid crystal in the nematic phase, a traveling light ray feels an effective metric, whose properties are linked to perpendicular and parallel refractive indexes, n
o and n
e respectively, of the rod-like molecule of the liquid crystal. As these indexes depend on the scalar order parameter of the liquid crystal, the Beris-Edwards hydrodynamic theory is used to connect the order parameter with the velocity of a liquid crystal flow at each point. This way we calculate a radial velocity profile that simulates the equatorial section of the Schwarzschild metric, in the region outside of Schwarzschild’s radius, in the nematic phase of the liquid crystal. In our model, the higher flow velocity can be on the order of some meters per second.










Physical description


1 - 8 - 2011
30 - 4 - 2011


  • Departamento de Física, CCEN, Universidade Federal da Paraíba, Cidade Universitária, 58051-900, João Pessoa, PB, Brazil
  • Departamento de Física, CCEN, Universidade Federal da Paraíba, Cidade Universitária, 58051-900, João Pessoa, PB, Brazil


  • [1] F. Moraes, Braz. J. Phys. 30, 304 (2000) http://dx.doi.org/10.1590/S0103-97332000000200011[Crossref]
  • [2] H. Kleinert, Gauge Fields in Condensed Matter, vol. 2 (World Scientific, Singapore, 1989)
  • [3] H. Kleinert, Multivalued Fields in Condensed Matter, Electromagnetism and Gravitation (World Scientific, Singapore, 2008)
  • [4] W.G. Unruh, Phys. Rev. Lett. 46, 1351 (1981) http://dx.doi.org/10.1103/PhysRevLett.46.1351[Crossref]
  • [5] M. Novello, M. Visser, G. Volovik, Artificial Black Holes (World Scientific, New Jersey, 2002) http://dx.doi.org/10.1142/9789812778178[Crossref]
  • [6] P.G. de Gennes, J. Prost, The Physics of Liquid Crystals, 2nd ed. (Claredon Press, Oxford, 1993)
  • [7] M. Kleman, O.D. Lavrentovich, Soft Matter Physics: An Introduction (Springer, New York, 2003)
  • [8] M. Kline, I.W. Kay, Electromagnetic theory and geometrical optics (Interscience, New York, 1965)
  • [9] C. Sátiro, F. Moraes, Eur. Phys. J. E 20, 173 (2006) http://dx.doi.org/10.1140/epje/i2005-10127-2[Crossref]
  • [10] C. Sátiro, F. Moraes, Eur. Phys. J. E 25, 425 (2008) http://dx.doi.org/10.1140/epje/i2008-10309-4[Crossref]
  • [11] A.M. de M. Carvalho, C. Sátiro, F. Moraes, Europhys. Lett. 80, 46002 (2007) http://dx.doi.org/10.1209/0295-5075/80/46002[Crossref]
  • [12] A.N. Beris, B.J. Edwards, Thermodynamics of Flowing Systems: with internal microstructure (Oxford University Press, Oxford, 1994)
  • [13] R. D’Inverno, Introducing Einstein’s Relativity (Oxford University Press, Oxford, 1998)
  • [14] M. Born, E. Wolf, Principles of Optics (Pergamon Press, London, 1980)
  • [15] J. Li, S. Gauza, S-T. Wu, J. Appl. Phys. 96, 19 (2004) http://dx.doi.org/10.1063/1.1757034[Crossref]
  • [16] I. Haller, Prog. Solid State Chem. 10, 103 (1975) http://dx.doi.org/10.1016/0079-6786(75)90008-4[Crossref]
  • [17] C. Denniston, E. Orlandini, J.M. Yeomans, Phys. Rev. E 63, 056702 (2001) http://dx.doi.org/10.1103/PhysRevE.63.056702[Crossref]
  • [18] P.D. Olmsted, C.-Y.D. Lu, Phys. Rev. E 56, R55 (1997) http://dx.doi.org/10.1103/PhysRevE.56.R55[Crossref]
  • [19] H. Cang, J. Li, V.N. Novikov, M.D. Fayer, J. Chem. Phys. 118, 9303 (2003) http://dx.doi.org/10.1063/1.1568338[Crossref]
  • [20] K. Rosquist, Gen. Relativ. Gravitation 36, 1977 (2004) http://dx.doi.org/10.1023/B:GERG.0000036055.82140.06[Crossref]
  • [21] C.W. Misner, K.S. Thorne, J.A. Wheeler, Gravitation (W.H. Freeman, San Francisco, 1973)
  • [22] P. Poulin, V. Cabuil, D.A. Weitz, Phys. Rev. Lett. 79, 4862 (1997) http://dx.doi.org/10.1103/PhysRevLett.79.4862[Crossref]

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