标题： 一个描述施瓦茨希尔德-梅尔文宇宙标量对应的精确解 显示英文标题

标题： An exact solution describing a scalar counterpart to the Schwarzschild-Melvin Universe

摘要： 施瓦茨希尔德-梅尔文时空是爱因斯坦电真空方程的一个精确解，描述了一个被磁场包围的黑洞，该磁场在远处与z轴对齐。 它在我们理解几何与物质之间的相互作用方面起着重要作用，并常被用作天体物理环境的替代模型。 在这里，我们构建了施瓦茨希尔德-梅尔文时空的标量对应物：一个非渐近平坦的黑洞几何结构，其标量场处处正则，且梯度在远处与z轴对齐。 显示英文摘要

摘要： The Schwarzschild-Melvin spacetime is an exact solution of the Einstein electrovacuum equations describing a black hole immersed in a magnetic field which is asymptotically aligned with the z-axis. It plays an important role in our understanding of the interplay between geometry and matter, and is often used as a proxy for astrophysical environments. Here, we construct the scalar counterpart to the Schwarzschild-Melvin spacetime: a non-asymptotically flat black hole geometry with an everywhere regular scalar field whose gradient is asymptotically aligned with the z-axis.