Dynamical analog spacetimes from nonlinear perturbations in a topological material

Abstract: Emergent spacetime analogs in condensed matter systems have opened a fascinating window into simulating aspects of gravitational physics in controlled laboratory environments. In this work, we develop a comprehensive nonlinear analog gravity framework within a topological material, incorporating the impact of Berry curvature on the hydrodynamic flow of electrons. Unlike prevalent studies in existing literature limited to linear perturbations, we derive and analyze a fully nonlinear wave equation governing radial perturbations of density and velocity fields, which dynamically generate an effective acoustic metric. Taking the example of graphene as a representative system, and calculating its properties from first principles, we numerically demonstrate the formation of evolving acoustic horizons and quantify analog Hawking temperatures in experimentally accessible regimes. Our findings suggest that topological materials can serve as versatile platforms to probe rich gravitational phenomena, including horizon dynamics and quasi-thermal emission, beyond conventional linear approximations. This work lays the groundwork for exploring nonlinear emergent spacetime in a broad class of quantum materials, bridging condensed matter physics and gravitational analogs.