Analysis of improved dynamics of nonrotating charged black holes

Abstract

We provide the quantization of a charged black hole. We consider a redefinition of the scalar constraint in order to render the algebra of constraints a Lie algebra. We apply loop quantum gravity techniques adhered to a novel improved dynamics scheme. We show that the model is solvable in closed form. We compute effective geometries, and show that the resulting effective space-times replace the inner horizon with a transition surface that connects trapped and antitrapped regions within the charged black hole interior. Quantum effects therefore stabilize the classical inner Cauchy horizons, as long as the charge is small compared to the mass. We further discuss the properties of these effective geometries by defining an effective stress-energy tensor out of the Einstein tensor, concluding that the null energy condition is violated.