On the lamppost model of accreting black holes

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.