Regular black holes: from non-linear electrodynamics to pure gravity models

It is well known that (static) regular black hole spacetimes can be sourced by appropriately chosen theories of non-linear electrodynamics. More recently, it was shown that many such models can also be obtained as solutions of vacuum gravity equations, upon considering an infinite series of quasi-topological higher-curvature corrections. After reviewing both these approaches, I will show that the latter construction can be upgraded to yield regular black holes with vanishing inner horizon surface gravity -- a necessary condition for the absence of classical instabilities associated with mass inflation on the inner horizon. I will also comment on singular charged black holes in theories with finite electromagnetic self-energy.