Mass inflation without Cauchy horizons

Mass inflation is a well established instability, conventionally associated to Cauchy horizons (which are also inner trapping horizons) of stationary geometries, leading to a divergent exponential buildup of energy. We show here that finite (but often large) exponential buildups of energy are generically present for dynamical geometries endowed with slowly-evolving inner trapping horizons, even in the absence of Cauchy horizons. This provides a more general definition of mass inflation based on quasi-local concepts. We also show that various known results in the literature are recovered in the limit in which the inner trapping horizon asymptotically approaches a Cauchy horizon. Our results imply that black hole geometries with non-extremal inner horizons, including the Kerr geometry in general relativity, and non-extremal regular black holes in theories beyond general relativity, can describe dynamical transients but not the long-lived endpoint of gravitational collapse.