Abstract
Abstract Mass inflation is a phenomenon occurring in the vicinity of the inner horizon in a spacetime with two horizons. It is shown that the mass of initially small perturbations grows exponentially as they approach the inner horizon. This implies that the inner horizon of a black hole is unstable under perturbations. Since mass inflation is determined by the surface gravities of the inner horizons, Carballo-Rubio et al. showed that if one makes the surface gravities of the inner horizons vanish, then the exponential growth associated with mass inflation is not present. Based on this conclusion, we look for the black hole solutions of multiple horizons in the presence of a nonlinear Maxwell field. We then make the inner horizons coincide with each other such that the surface gravities of all inner horizons vanish. In this way, black holes with multiple horizons without mass inflation are constructed.