Microscopic 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 exhibits very unusual 2+2-dimensional spatiotemporal dynamics. Here we report a detailed microscopic study of mutual interactions of individual self-focused optical filaments inside this metamaterial. In agreement with theoretical expectations, the observed mutual interactions of individual filaments exhibit strong similarities with general relativity in 2+1 dimensions. This observation is very important since 2+1-dimensional gravity is an exactly solvable theory even in the quantum gravity limit.