Abelian-Higgs模型中的精确\textit{pp}波、（A）dS波和Kundt空间
Exact \textit{pp}-waves, (A)dS waves and Kundt spaces in the Abelian-Higgs model
摘要：
我们找到了耦合到广义相对论的阿贝尔-希格斯模型的新的精确解，其特征在于非零超导电流。这些解对应于\textit{pp}波、AdS波和Kundt空间，对于这些空间，麦克斯韦场和标量的相位梯度都与定义这些空间的零方向对齐。在孔特族中，与超导电流正交的二维表面的几何形状由二维刘维尔方程的解确定，因此，这些表面具有常曲率，因为它发生在真空中。刘维尔方程的解也作为麦克斯韦场的势，我们将其积分为封闭形式。利用这些结果，我们表明，引力和标量相互作用的组合效应可以限制在一个有界区域内的表面横向电流的电磁场。
英文摘要：
We find new exact solutions of the Abelian-Higgs model coupled to General Relativity, characterized by a non-vanishing superconducting current. The solutions correspond to \textit{pp}-waves, AdS waves, and Kundt spaces, for which both the Maxwell field and the gradient of the phase of the scalar are aligned with the null direction defining these spaces. In the Kundt family, the geometry of the two-dimensional surfaces orthogonal to the superconducting current is determined by the solutions of the two-dimensional Liouville equation, and in consequence, these surfaces are of constant curvature, as it occurs in a vacuum. The solution to the Liouville equation also acts as a potential for the Maxwell field, which we integrate into a closed-form. Using these results, we show that the combined effects of the gravitational and scalar interactions can confine the electromagnetic field within a bounded region in the surfaces transverse to the current.
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