# Vaidya spacetimes, black-bounces, and traversable wormholes

## TL;DR

This paper introduces a dynamic Vaidya-like metric for regular black-bounce and traversable wormhole geometries, enabling the study of transitions between black-bounces and wormholes in evolving spacetimes.

## Contribution

It extends static black-bounce and wormhole models to non-static, evolving spacetimes using Vaidya-like coordinates, allowing analysis of their dynamic transitions.

## Key findings

- The metric describes evolving black-bounce and wormhole geometries.
- It models transitions between black-bounces and wormholes.
- The approach is tractable for physical scenarios involving spacetime evolution.

## Abstract

We consider a non-static evolving version of the regular "black-bounce"/traversable wormhole geometry recently introduced in JCAP02(2019)042 [arXiv:1812.07114 [gr-qc]]. 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 \[ ds^{2}=-\left(1-\frac{2m(w)}{\sqrt{r^{2}+a^{2}}}\right)dw^{2}-(\pm 2 \,dw \,dr) +\left(r^{2}+a^{2}\right)\left(d\theta^{2}+\sin^{2}\theta \;d\phi^{2}\right). \] Here $w=\{u,v\}$ denotes the $\{outgoing,ingoing\}$ null time coordinate; representing $\{retarded,advanced\}$ time. This spacetime is still simple enough to be tractable, and neatly interpolates between Vaidya spacetime, a black-bounce, 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 black-bounce to wormhole transition.