Note on the Angular Momentum and Mass of Gravitational Geons

It is shown that (1) the angular momentum of a gravitational geon must be zero if it is axisymmetric and (2) the mass of a gravitational geon must be zero if it is stationary, i.e., if the space-time possesses a Killing vector which is timelike at infinity. Here angular momentum and mass are defined in terms of the asymptotic form of the metric at large distances; they are physical quantities which can be experimentally measured by distant observers. Since the gravitational geons previously considered are highly dynamical on a small scale, our result on the vanishing mass of a stationary geon does not conflict with previous analyses showing that gravitational geons can have mass. Similarly, our results do not exclude the possibility of gravitational geons having nonvanishing angular momentum if they are not strictly axisymmetric.