Extraordinary rays in a hyperbolic metamaterial behave as particle world lines in a three-dimensional (2 + 1) Minkowski spacetime. We analyze electromagnetic field behavior at the boundaries of this effective spacetime depending on the boundary orientation. If the boundary is perpendicular to the spacelike direction in the metamaterial, an effective Rindler horizon may be observed, which produces Hawking radiation. On the other hand, if the boundary is perpendicular to the timelike direction, the system undergoes a phase transition to a state with a different nature of the spacetime, with nonintegrable field divergence at the transformation point. Experimental observations of the transition using plasmonic metamaterials confirm this conclusion
