Regular isolated black holes

We review a recently introduced¹ approach to study spacetimes which contain an isolated black hole. We allow for gravitational radiation to fall through the event horizon and/or to be radiated at infinity. The crucial idea in our setting is the introduction of physical coordinates that have the meaning of being null hypersurfaces near the horizon and in a neighborhood of future null infinity. These spacetimes have remarkable properties, as for example a generalized notion of surface gravity κ_H.