Abstract
The golden dream of those who study the quantum black hole physics is to obtain the self-consistent quantum description of the evaporating black hole. The direct way to attack this problem is to use the effective action of quantum gravity, which in principle contains all the necessary information. But not speaking even about the well-known troubles connected with the nonrenormalizability of quantum gravity this way is not simple because one cannot calculate the effective action exactly even in the one-loop approximation. Thus we have to single out the terms of the effective action which are most important for the problem under consideration. For example, if we discuss the problem of singularities inside the black holes, the most important terms are those with the highest-order derivatives. Such an approach, developed in the works by Vilkovisky and the present author1,2 led to certain conclusions about the removal of singularities inside the black holes. In particular, it was proved that for small masses \( M(M\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{ < } {m_{p\ell = }}\sqrt {h'c/G} \approx {10^{ - 5}}g)\) the effects of quantum gravity destroy not only the singularity but also the black hole itself. This means that for small masses the vacuum polarization effects do not allow the gravitational field to be strong enough to form an apparent horizon: consequently the event horizon dos not arise.
Keywords
Black Hole Quantum Gravity Event Horizon Apparent Horizon Lebedev Physical InstitutePreview
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