Gravitational edge mode powers galaxy flat rotation curves

Abstract

The point-particle approximation is foundational to modelling clustering of matter in the universe, but is fundamentally inconsistent within General Relativity due to associated spacetime singularities. This bottleneck has historically restricted the study of matter clustering to linear scales. We resolve this by utilising the recent observation that a matter horizon precedes the formation of caustics in expanding spacetimes. This allows for the isolation of singularities via spacetime surgery. By glueing distinct spacetime sheets related by a discrete transformation across the shared boundary, we derive a covariant backreaction term that contributes to the effective energy-momentum tensor. Crucially, we identify this backreaction contribution with gravitational edge modes; physical degrees of freedom residing on boundaries that arise from the breaking of the diffeomorphism group. These gravitational edge modes modify local particle trajectories, naturally producing flat galaxy rotation curves in the outskirts without invoking dark matter particles. Our framework thus demonstrates that gravitational edge modes can act as effective dark matter, offering a first-principles alternative to particle dark matter for explaining galactic dynamics.