Gravitational anyon

Abstract

We show that, in the (2+1)-dimensional Einstein gravity without the Chern-Simons term, the topological interaction of a point source with or without spin necessarily makes the composite state of the source and neutral test particle a gravitational anyon. In particular for a massless spinning source with spin $\ensuremath{\sigma}$, the angular momentum $l$ of the gravitational anyon is given by $l=n\ensuremath{-}\frac{\ensuremath{\sigma}E}{2\ensuremath{\pi}}$, where $E$ is the energy and $n$ is an integer.