Building a black hole-wormhole-black hole combination

Abstract

In this paper, we present the spherically symmetric Proca star in the presence of a phantom field and obtain a traversable wormhole solution for non-trivial topological spacetime. Using numerical methods, symmetric solutions and asymmetric solutions are obtained in two asymptotically flat regions. We find that when changing the throat size $r_0$, both the mass $M$ and the Noether charge $Q$ no longer have the spiral characteristics of an independent Proca star, furthermore, the asymmetric solution can be turned into the symmetric solution at some frequency $\ddot{I}‰$ in certain $r_0$. In particular, we find that when the frequency takes a certain value, for each solution, there is an extremely approximate black hole solution, and there is even a case where an event horizon appears on both sides of the wormhole throat.

32 pages, 19 figures