IX Black Hole Workshop

Guimarães 19-20 December 2016

The distinguished role of extremal horizons is beyond any doubts. It is sufficient to mention briefly such issues as black hole entropy, the scenarios of evaporation including the nature of remnants, etc. Meanwhile, although such object appear naturally on the pure classical level (the famous examples is the Reissner-Nordstr"{o}m black hole with the mass equal to charge), the question of their existence becomes non-trivial in the semiclassical case, when backreaction of quantum fields (whatever weak it be) is taken into account. This is due to the fact that the quantum-corrected metric contains some combinations of the stress-energy tensor having the meaning of the energy measured by a free-falling observer that potentially may diverge near the extremal horizon. However, numerical calculations showed that such divergencies do not occur for massless fields in the Reissner-Nordstr"{o}m background \cite{andRN}. Analytical studies for massive quantized fields \cite{MZ2} gave the same result. Then they have been extended to so called ultraextremal horizons \cite{MZ1} when the metric coefficient $ -g_{tt} \sim (r_{+}-r)^{3} \label{n} $ near the horizon (here $ is the Schwarzschild-like coordinate, =r_{+}$ corresponds to the horizon). Such horizons are encountered, for example, in the Reissner-Nordstr"{o}m-de Sitter solution, when the cosmological constant $\Lambda >0$ \cite{Romans}. In doing so, it turns out that the horizon is of cosmological nature, so $ approach {+}$ from r.