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 present for dynamical geometries describing accreting black holes with slowly evolving inner trapping horizons, even in the absence of Cauchy horizons. The explicit evaluation of the adiabatic conditions behind these exponential buildups shows that this phenomenon is universally present for physically reasonable accreting conditions. This noneternal mass inflation does not require the introduction of global spacetime 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 nonextremal inner horizons, including the Kerr geometry in general relativity, and nonextremal regular black holes in theories beyond general relativity, can describe dynamical transients but not the long-lived end point of gravitational collapse.