  We consider the class of metrics that can be obtained from those of
nonextreme black holes by limiting transitions to the extreme state such that
the near-horizon geometry expands into a whole manifold. These metrics include,
in particular, the Rindler and Bertotti - Robinson spacetimes. The general
formula for the entropy of massless radiation valid either for black-hole or
for acceleration horizons is derived. It is argued that, as a black hole
horizon in the limit under consideration turns into an acceleration one, the
thermodynamic entropy $S_{q}$ of quantum radiation is due to the Unruh effect
entirely and $S_{q}=0$ exactly. The contribution to the quasilocal energy from
a given curved spacetime is equal to zero and the only nonvanishing term stems
from a reference metric. In the variation procedure necessary for the
derivation of the general first law, the metric on a horizon surface changes
along with the boundary one, and the account for gravitational and matter
stresses is an essential ingredient of the first law. This law confirms the
property $S_{q}=0$. The quantum-corrected geometry of the Bertotti - Robinson
spacetime is found and it is argued that backreaction of quantum fields mimics
the effect of the cosmological constant $\Lambda_{eff\text{}}$ and can
drastically 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 the
quantum versions of the cold and ultracold limits of the Reissner-Nordstrom-de
Sitter metric.
