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}=-left(1-frac{2m}{sqrt{r^{2}+a^{2}}}right)dt^{2}+frac{dr^{2}}{1-frac{2m}{sqrt{r^{2}+a^{2}}}} +left(r^{2}+a^{2}right)left(dtheta^{2}+sin^{2}theta ;dphi^{2}right). ] 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.
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