Study of Effective 2+1 Dimensional Gravity in Ferrofluid-Based Hyperbolic Metamaterials

Recent theoretical and experimental work demonstrated that nonlinear optics of ferrofluid-based hyperbolic metamaterials exhibit very unusual spatiotemporal dynamics. Here a detailed theoretical and experimental study of mutual interactions of individual self-focused optical filaments inside this metamaterial is reported. In agreement with theoretical expectations, the observed mutual interactions of individual filaments exhibit strong similarities with general relativity in 2+1 dimensions, which predicts that these interactions must have predominantly non-Newtonian topological character. This observation is important since 2+1-dimensional gravity is an exactly solvable theory even in the quantum gravity limit.