Resolution of Reissner–Nordström singularities by higher-derivative corrections

Abstract

We describe a non-minimal higher-derivative extension of Einstein-Maxwell theory in which electrically-charged black holes and point charges have globally regular gravitational and electromagnetic fields. We provide an exact static, spherically symmetric solution of this theory that reduces to the Reissner-Nordström one at weak coupling, but in which the singularity at r = 0 is regularized for arbitrary mass and (non-vanishing) charge. We discuss the properties of these solutions and comment on the physical significance of our results.

Regular black holes in three dimensions

“…Inspired by their higher-dimensional counterparts [94,95], we define "Electromagnetic Gen-eralized Quasitopological gravities" (EM-GQT) in three dimensions by the condition that a general Lagrangian |g|L[g ab , R ab , ∂ a φ] becomes a total derivative when evaluated on the ansatz [99]…”

“…Our construction here relies on a set of ideas that have been successfully applied to the construction of black hole solutions in higher-dimensions [79][80][81][82][83][84][85][86][87][88][89][90][91][92][93][94][95][96][97]. The theories involved possess particularly simple static black hole solutions, characterized by a single function which, in some cases, satisfies an algebraic equation.…”

“…While the approach was first developed for purely gravitational theories, certain ad-ditional fields turn out to fit naturally within the framework. In four dimensions, the natural choice is a "magnetic ansatz" for a Maxwell field, which automatically satisfies the equations of motion of general non-minimally coupled higher-curvature theories and at the same time has a non-trivial effect on the metric -yet simple enough to allow for fully analytic solutions [94,95]. In three dimensions, the analogous magnetic rôle is played by ∂ a φ -where φ is a real scalar-which is related to the Maxwell field strength via a duality transformation.…”

Correlation of Horizons and Black Hole Thermodynamics

“…Motivated by the higher dimensional counterparts [12,13], the Electromagnetic Generalized Quasitopological gravities (EMG-QT) in three dimensions, are defined with the condition that a general Lagrangian of the form |g|L[g ab , R ab , ∂ a φ] can be written in a total derivative, when evaluated on the ansatz [14]- [16]…”

Regular black holes in three dimensions

“…Our construction here relies on a set of ideas that have been successfully applied to the construction of black hole solutions in higher-dimensions [81][82][83][84][85][86][87][88][89][90][91][92][93][94][95][96][97][98][99]. The theories involved possess particularly simple static black hole solutions, characterized by a single function which, in some cases, satisfies an algebraic equation.…”