Black-bounce to traversable wormhole

So-called regular black holes are a topic currently of considerable interest in the general relativity and astrophysics communities. Herein we investigate a particularly interesting regular black hole spacetime described by the line element ds(2) = -(1 - 2m/root r(2) + a(2)) dt(2) + dr(2)/1 - 2m/root r(2)+a(2) + (r(2) + a(2)) (d theta(2) + sin(2) theta d phi(2)). This spacetime neatly interpolates between the standard Schwarzschild black hole and the Morris-Thorne traversable wormhole; at intermediate stages passing through a black-bounce (into a future incarnation of the universe), an extremal null-bounce (into a future incarnation of the universe), and a traversable wormhole. As long as the parameter a is non-zero the geometry is everywhere regular, so one has a somewhat unusual form of regular black hole, where the origin r = 0 can be either spacelike, null, or timelike. Thus this spacetime generalizes and broadens the class of regular black holes beyond those usually considered.