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We consider the class of metrics that can be obtained from those ofnonextreme black holes by limiting transitions to the extreme state such thatthe near-horizon geometry expands into a whole manifold. These metrics include,in particular, the Rindler and Bertotti - Robinson spacetimes. The generalformula for the entropy of massless radiation valid either for black-hole orfor acceleration horizons is derived. It is argued that, as a black holehorizon in the limit under consideration turns into an acceleration one, thethermodynamic entropy $S_{q}$ of quantum radiation is due to the Unruh effectentirely and $S_{q}=0$ exactly. The contribution to the quasilocal energy froma given curved spacetime is equal to zero and the only nonvanishing term stemsfrom a reference metric. In the variation procedure necessary for thederivation of the general first law, the metric on a horizon surface changesalong with the boundary one, and the account for gravitational and matterstresses is an essential ingredient of the first law. This law confirms theproperty $S_{q}=0$. The quantum-corrected geometry of the Bertotti - Robinsonspacetime is found and it is argued that backreaction of quantum fields mimicsthe effect of the cosmological constant $\Lambda_{eff\text{}}$ and candrastically change the character of spacetime depending on the sign of $\Lambda_{eff}$ --- for instance, turn $AdS_{2}\times S_{2}$ into $dS_{2}\times S_{2}$or $Rindler_{2}\times S_{2}$. Two latter solutions can be thought of as thequantum versions of the cold and ultracold limits of the Reissner-Nordstrom-deSitter metric.Comment: 27 pages, REVTeX 3.0. Expanded from previous version. Title somewhat  changed. Qualitative explanation of effects of strong quantum backreaction on  geometry suggested in terms of induced cosmological constant. Stressed that  if this constant is positive, solutions found can be considered as quantum  versions of charged Nariai one. Accepted for publication in Class. Quant.  Gra

Non-extreme black holes near the extreme state and acceleration horizons: thermodynamics and quantum-corrected geometry