On The Regularized McVittie Black Bounce and a Family of Traversable Wormholes

The McVittie metric describes a self-gravitating compact object embedded in an expanding universe. It inherits two singularities: a curvature singularity at $r\to 0$ and a cosmological singularity at $a(t)\to 0$. Motivated by the construction of black-bounce geometries, we regularize both of these singularities and propose a regularized McVittie metric. The central singularity is regularized by replacing $r\to \sqrt{r^2+b^2}$, leading to a geometry that interpolates between a cosmological black hole, a black bounce, and a traversable wormhole. Similarly, the cosmological singularity is regularized by introducing a non-vanishing scale factor $a\to \sqrt{a^2+a_b^2}$. The resulting spacetime is supported by an effective imperfect fluid with finite anisotropic stress. We investigate the formation of the apparent horizon, analyze the circular geodesic structure, and argue that the geometry can also be interpreted as a conformally evolving Morris-Thorne wormhole embedded in a regular cosmological background.