Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1994-07-26
Phys.Rev. D51 (1995) 2813-2826
Physics
High Energy Physics
High Energy Physics - Theory
LaTeX, 27pp, one uuencoded figure (A few sentences are rephrased to prevent a possible confusion; an extra paragraph Commentin
Scientific paper
10.1103/PhysRevD.51.2813
Pair-production of magnetic Reissner-Nordstr\"{o}m black holes (of charges $\pm q$) was recently studied in the leading WKB approximation. Here, we consider generic quantum fluctuations in the corresponding instanton geometry given by the Euclidean Ernst metric, in order to simulate the behaviour of the one-loop tunneling rate. A detailed study of the Ernst metric suggests that for sufficiently weak field $B$, the problem can be reduced to that of quantum fluctuations around a single near-extremal Euclidean black hole in thermal equilibrium with a heat bath of finite size. After appropriate renormalization procedures, typical one-loop contributions to the WKB exponent are shown to be inversely proportional to $B$, as $B\rightarrow 0$, indicating that the leading Schwinger term is corrected by a small fraction $\sim \hbar /q^2$. We demonstrate that this correction to the Schwinger term is actually due to a semiclassical shift of the black hole mass-to-charge ratio that persists even in the extremal limit. Finally we discuss a few loose ends.
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