Classification of global structures of evaporating regular black holes with infinite periods of time

Abstract

We carry out model independent analyses for global structures of spherically symmetric regular black holes that evaporate and approach the extremal state spending infinite periods of time due to Hawking radiation. We assume the radius of the outer apparent horizon (outer AH) to be a decreasing function of ingoing null coordinate, and consider the three cases, Cases 1, 2, and 3, where the radius of the inner AH is a constant, increases, and decreases, respectively. A complete classification of the Penrose diagrams is presented in each case, taking account not only of the presence and absence of the event horizon but also of the relative positions of the inner and outer AHs. Sufficient conditions that lead to each type are proved, and the examples of each type are summarized. We also study the behavior of outgoing null geodesics in models where the null geodesic equation is solvable, and figure out the important factors to determine the type of a spacetime using concepts in the area of dynamical systems. The formation of a Cauchy horizon is also established in the solvable models when the event horizon is present.