Another system that can model curved space times (and singularities) is a simple chain of coupled pendula, or alternatively a long Josephson junction, which has

Another system that can model curved space times (and singularities) is a simple chain of coupled pendula, or alternatively a long Josephson junction, which has the same equation of motion. The system can have a soliton solution (a 360 degree twist in the chain) that travels along the chain. The spacetime curvature along the soliton (i.e. the frequency dispersion relation for small harmonic waves on top of the solution) exhibits an event horizon. But like with the other system, the analogy does not teach us anything novel about curved spacetimes, though it can allow for some interesting phenomena.