Abstract
We consider quantum effects of gravitational and electromagnetic fields in spherically symmetric black hole spacetimes in the asymptotic safety scenario. Introducing both the running gravitational and electromagnetic couplings from the renormalization group equations and applying a physically sensible scale identification scheme based on the Kretschmann scalar, we construct a quantum mechanically corrected, or quantum improved Reissner-Nordstrom metric. We study the global structure of the quantum improved geometry and show, in particular, that the central singularity is resolved, being generally replaced with a regular Minkowski-core, where the curvature tensor vanishes. Exploring cases with more general scale identifications, we further find that the space of quantum improved geometries is divided into two regions: one for geometries with a regular Minkowski-core and the other for those with a weak singularity at the center. At the boundary of the two regions, the geometry has either Minkowski-, de Sitter-, or anti-de Sitter(AdS)-core.
Highlights
The occurrence of a spacetime singularity under complete gravitational collapse is a robust prediction of general relativity, as the singularity theorem asserts [1]
We consider quantum effects of gravitational and electromagnetic fields in spherically symmetric black hole spacetimes in the asymptotic safety scenario
We have studied the quantum improvement of the charged spherically symmetric black hole spacetimes in the asymptotic safety scenario
Summary
The occurrence of a spacetime singularity under complete gravitational collapse is a robust prediction of general relativity, as the singularity theorem asserts [1]. We consider the problem of singularity resolution by examining yet another quantum improved black hole including the running gravitational as well as Uð1Þ gauge couplings: that is, the “quantum improved Reissner-Nordstrom metric,” as a first step toward understanding fundamental interactions all together in the asymptotic safety scenario. For this purpose, we need to address the following two issues: First, when taking into account quantum effects of the electromagnetic field, one has to deal with Landau poles, which involve the (logarithmic) divergence of the running Uð1Þ gauge coupling at a finite momentum scale.
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