Equatorial circular orbits of some static gravitational fields with naked singularities

We investigate the equatorial circular orbits in the Weyl metrics with naked singularities. We find that in many Weyl fields, as well as in the Reissner-Nordstr\"om $e>m$ metric, there are equatorial equilibrium regions corresponding to large gravitational red shifts at infinity. However, except in the Reissner-Nordstr\"om case, such regions are unstable. Thus these solutions might not be very realistic models of large-red-shift objects. On the other hand, it is likely that there may be gravitational-synchrotron-radiation orbits in the Weyl metrics. These and other properties of naked singularities indicate that they should be studied more closely for possible roles in exotic astrophysical phenomena.