Flowing liquid crystal simulating the Schwarzschild metric |
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Authors: | Erms R Pereira and Fernando Moraes |
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Institution: | (1) Russian Academy of Sciences Inst. Crystallography, Leninskii prospect 69, 119333 Moscow, Russia; |
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Abstract: | 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. |
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Keywords: | |
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