Truly Naked Black Holes and Quasi-black Holes

Usually, a black hole horizon hides singularities beyond it, being itself perfectly regular. We discuss somewhat unusual cases when the system can combine regular and singular features due to the presence of the horizon. The first example concerns the so-called truly naked black holes, when the Kretschmann scalar is finite but tidal forces diverge at the horizon in the freely falling frame. The second one concerns the so-called quasi-black holes, a special kind of objects on the verge of forming extremal black holes. Then, a "naked" behavior can occur in the entire region beyond the quasi-horizon. Apart from this, there is another kind of singular behavior in this case due to the quasi-horizon. In particular, this concerns the simplest example with a charged massive shell empty inside. The curvature inside is zero, but the whole inner region becomes degenerate in the quasi-horizon limit.