# Black-bounce to traversable wormhole

## TL;DR

This paper explores a spacetime model that smoothly transitions between a regular black hole, a null-bounce, and a traversable wormhole, broadening the understanding of regular black hole geometries in general relativity.

## Contribution

It introduces a new spacetime metric that unifies black holes and wormholes, extending the class of regular black hole solutions with a parameter-controlled transition.

## Key findings

- The spacetime is regular everywhere for non-zero parameter a.
- It interpolates between Schwarzschild black hole and Morris-Thorne wormhole.
- The geometry allows for different causal structures at the origin.

## Abstract

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 \[ ds^{2}=-\left(1-\frac{2m}{\sqrt{r^{2}+a^{2}}}\right)dt^{2}+\frac{dr^{2}}{1-\frac{2m}{\sqrt{r^{2}+a^{2}}}} +\left(r^{2}+a^{2}\right)\left(d\theta^{2}+\sin^{2}\theta \;d\phi^{2}\right). \] 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.