Flowing Liquid Crystal Simulating the Schwarzschild Metric

TL;DR

This paper demonstrates how a flowing liquid crystal can simulate the equatorial Schwarzschild metric by linking its flow velocity and refractive indexes to the properties of spacetime curvature.

Contribution

It introduces a novel method to emulate black hole spacetime geometry using liquid crystal flow and optical properties, connecting hydrodynamics with general relativity.

Findings

Radial velocity profile simulates Schwarzschild metric outside the event horizon.

Flow velocities can reach several meters per second.

Effective metric properties are linked to liquid crystal refractive indexes.

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, $n_o$ e $n_e$ 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 of the order of some meters per second.