Statistics and general relativity

Abstract

There exists a class of particle-like topological excitations in generally covariant theories called geons, discussed by Friedman and Sorkin, and by these authors, and others. Here, we show by specific examples that certain of these geons can be so quantized that they are characterized by no definite statistics. For instance, three-dimensional geons may be neither bosons nor fermions (nor paraparticles). It can also happen, as pointed out before by Sorkin, and as we briefly discuss here, that a tensorial (spinorial) goen obeys Fermi (Bose) statistics. Our usual conceptions about the statistics of particle species thus do not seem to be valid in generally covariant theories, at least without further physical inputs such as, perhaps, the possibility of topology change.