Vaidya spacetimes, black-bounces, and traversable wormholes

Abstract

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 (à la Vaidya). The spacetime metric is ds2=−1− 2m(w) √r2+a2 dw2−(±2dwdr)+r2+a2 dθ2+sin2θdφ2 . Here w={u,v} denotes suitably defined {outgoing,ingoing} null time coordinates; representing {retarded,advanced} time, while, (at least for a=0), we allow r∈(−∞,+∞). 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.