  The application of the virial theorem provides a tool to estimate
supermassive black hole (BH) masses in large samples of active galactic nuclei
(AGN) with broad emission lines at all redshifts and luminosities, if the broad
line region (BLR) is gravitationally bound. In this paper we discuss the
importance of radiation forces on BLR clouds arising from the deposition of
momentum by ionizing photons. Such radiation forces counteract gravitational
ones and, if not taken into account, BH masses can be severely underestimated.
We provide virial relations corrected for the effect of radiation pressure and
we discuss their physical meaning and application. If these corrections to
virial masses, calibrated with low luminosity objects, are extrapolated to high
luminosities then the BLRs of most quasars might be gravitationally unbound.
The importance of radiation forces in high luminosity objects must be
thoroughly investigated to assess the reliability of quasar BH masses.
