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We analyze the rather unusual properties of some exact solutions in 2Ddilaton gravity for which infinite quantum stresses on the Killing horizon canbe compatible with regularity of the geometry. In particular, the Boulwarestate can support a regular horizon. We show that such solutions are containedin some well-known exactly solvable models (for example, RST). Formally, theyappear to account for an additional coefficient $B$ in the solutions (for thesame Lagrangian which contains also ''traditional'' solutions) that gives riseto the deviation of temperature $T$ from its Hawking value $T_{H}$. TheLorentzian geometry, which is a self-consistent solution of the semiclassicalfield equations, in such models, is smooth even at $B\neq 0$ and there is noneed to put B=0 ($T=T_{H}$) to smooth it out$.$ We show how the presence of$B\neq 0$ affects the structure of spacetime. In contrast to ''usual'' blackholes, full fledged thermodynamic interpretation, including definite value ofentropy, can be ascribed (for a rather wide class of models) to extremalhorizons, not to nonextreme ones. We find also new exact solutions for''usual'' black holes (with $T=T_{H}$). The properties under discussion arisein the \QTR{it}{weak}-coupling regime of the effective constant ofdilaton-gravity interaction. Extension of features, traced in 2D models, to 4Ddilaton gravity leads, for some special models, to exceptional nonextreme blackholes having no own thermal properties.Comment: 43 pages, To appear in "Bekenstein Issues" of Foundations of Physic

foundations of physics

Regular self-consistent geometries with infinite quantum backreaction in 2D dilaton gravity and black hole thermodynamics: unfamiliar features of familiar models