  We study the lamppost model, in which the X-ray source in accreting
black-hole systems is located on the rotation axis close to the horizon. We
point out a number of inconsistencies in the widely used lamppost model
relxilllp, e.g., the neglect of the redshift of the photons emitted by the
lamppost and directly observed. They appear to invalidate those model fitting
results for which the source distances from the horizon are within several
gravitational radii. Furthermore, if those results were correct, most of the
photons produced in the lamppost would be trapped by the black hole, and the
luminosity generated in the source as measured at infinity would be much larger
than that observed. This appears to be in conflict with the observed smooth
state transitions between the hard and soft states of X-ray binaries. The
required increase of the accretion rate and the associated efficiency reduction
present also a problem for AGNs. Then, those models imply the luminosity
measured in the local frame to be much higher than that produced in the source
and measured at infinity, due to the additional effects of time dilation and
redshift, and the electron temperature to be higher significantly than that
observed. We show that these conditions imply that the fitted sources would be
out of the pair equilibrium. On the other hand, the above issues pose
relatively minor problems for sources at large distances from the black hole,
where relxilllp can still be used.
