Robotic active matter on a deformable surface generates an analog gravity system

Many analog gravity models of general relativity (GR) have been developed (e.g. in fluids and Bose-Einstein condensates) with goals to probe GR-like phenomena in the laboratory. One common analog is to study the dynamics of freely moving objects (like marbles) on two-dimensional curved or elastic sheets. Such systems have issues which prevent them from functioning as analog gravity models, including dominance of Earth’s gravity over metric dynamics, the inability to model time-like curvature effects, and dissipation which limits persistent dynamics. Here, we circumvent these issues by developing an exact analog gravity system based on an active matter system: a robot car driving on a deformable membrane. We observe qualitative GR-like features including circular and precessing orbits around a central depression. We extract a dynamical system that describes our experiments. Remarkably it is the self-propelled aspects of the car that allow a formal mapping to Einstein’s equations in 2+1 dimensions, thus creating an accurate GR model whose parameters can be tuned to mimic different astrophysical situations (e.g. Schwarzschild metric around a black hole).