Novel black-bounce spacetimes: Wormholes, regularity, energy conditions, and causal structure

We develop a number of novel "black-bounce" spacetimes. These are specific regular black holes where the area radius always remains nonzero, thereby leading to a "throat" that is either timelike (corresponding to a traversable wormhole), spacelike (corresponding to a "bounce" into a future universe), or null (corresponding to a "one-way wormhole"). We first perform a general analysis of the regularity conditions for such a spacetime and then consider a number of specific examples. The examples are constructed using a mass function similar to that of Fan-Wang and fall into several particular cases, such as the original Simpson-Visser model, a Bardeen-type model, and other generalizations thereof. We analyze the regularity, energy conditions, and causal structure of these models. The main results are several new geometries, more complex than before, with two or more horizons, with the possibility of an extremal case. We derive a general theorem regarding static spacetime regularity and another general theorem regarding (non)satisfaction of the classical energy conditions.