Vaidya spacetimes, black-bounces, and traversable wormholes

We consider a non-static evolving version of the regular black-bounce'/traversable wormhole geometry recently introduced in Simpson and Visser (2019 J. Cosmol. Astropart. Phys. JCAP02(2019)042). We first re-write the static metric using Eddington-Finkelstein coordinates, and then allow the mass parameter m to depend on the null time coordinate (a la Vaidya). The spacetime metric is ds(2) = - (1 - 2m(w)/root r(2)+a(2)) dw(2) - (+/- 2dw dr) + (r(2) + a(2)) (d theta(2) + sin(2)theta d phi(2)). Here w = {u, v} denotes suitably defined {outgoing, ingoing} null time coordinates; representing {retarded, advanced} time, while, (at least for a not equal 0), we allow r is an element of (-infinity,+infinity). This spacetime is still simple enough to be tractable, and neatly interpolates between Vaidya spacetime, a blackbounce, and a traversable wormhole. We show how this metric can be used to describe several physical situations of particular interest, including a growing black-bounce, a wormhole to black-bounce transition, and the opposite blackbounce to wormhole transition.