A common argument suggests that non-singular geometries may not describe black holes observed in nature since they are unstable due to a mass-inflation effect. We analyze the dynamics associated with spherically symmetric, regular black holes taking the full backreaction between the infalling matter and geometry into account. We identify the crucial features taming the growth of the mass function and a diminished curvature singularity at the Cauchy horizon and demonstrate that the regular black hole solutions proposed by Hayward and obtained from Asymptotic Safety satisfy these properties.
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