Toward One-Loop Tunneling Rates of Near-Extremal Magnetic Black Hole Pair-Production

Abstract

Pair-production of magnetic Reissner-Nordström 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 $B\to 0$, indicating that the leading Schwinger term is corrected by a small fraction $\sim \hslash /q^2$. 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.

LaTeX, 27pp, one uuencoded figure (A few sentences are rephrased to prevent a possible confusion; an extra paragraph Commenting on the strictly extremal case is added.)

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• Quantum Stability of Accelerated Black Holes
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• Quantum Corrections to Pair Production of Charged Black Holes in de Sitter Space
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• Magnetic Black Hole Pair-Production: One-Loop Tunneling Rate in the Weak Field Limit