标题： 构建一个黑洞-虫洞-黑洞组合 显示英文标题

标题： Building a black hole-wormhole-black hole combination

摘要： 在本文中，我们提出了存在幻影场情况下的球对称Proca星，并获得了非平凡拓扑时空的可穿越虫洞解。 使用数值方法，在两个渐近平坦区域中得到了对称解和不对称解。 我们发现，当改变喉部尺寸$r_{0}$时，质量$M$和诺特定理电荷$Q$不再具有独立Proca星的螺旋特性，此外，在某些频率$\omega$下，不对称解可以转化为对称解，在某些$r_{0}$中。 特别是，我们发现当频率取某个值时，对于每个解，都存在一个极其近似的黑洞解，甚至存在虫洞喉部两侧都出现事件视界的案例。 显示英文摘要

摘要： 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 $\omega$ 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.