Proca stars in wormhole spacetime

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 ADM mass M and the Noether charge Q no longer have the spiral characteristics of a classic Proca star, furthermore, the asymmetric solution can be turned into the symmetric solution at some frequency ω in certain r 0 . In particular, we find that when the frequency takes a certain value, the similar “black-bounce” structure will appear.