Quantum backreaction of massive fields and self-consistent semiclassical extreme black holes and acceleration horizons

We consider the effect of backreaction of quantized massive fields on the metric of extreme black holes (EBH). We find the analytical approximate expression for the stress-energy tensor for a scalar (with an arbitrary coupling), spinor and vector fields near an event horizon. We show that, independent of a concrete type of EBH, the energy measured by a freely falling observer is finite on the horizon, so that quantum backreaction is consistent with the existence of EBH. For the Reissner-Nordstrom EBH with a total mass M_{tot} and charge Q we show that for all cases of physical interest M_{tot}< Q. We also discuss different types of quantum-corrected Bertotti-Robinson spacetimes, find for them exact self-consistent solutions and consider situations in which tiny quantum corrections lead to the qualitative change of the classical geometry and topology. In all cases one should start not from a classical background with further adding quantum corrections but from the quantum-corrected self-consistent geometries from the very beginning.