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arXiv 1707.02802gr-qchep-th
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黑洞引力场中的暗物质宇宙弦

Dark matter cosmic string in the gravitational field of a black hole

Łukasz Nakonieczny, Anna Nakonieczna, Marek Rogatko

摘要:

我们分析研究并提出了一个数值模型的阿贝尔希格斯暗物质涡在一个固定的轴对称克尔黑洞的时空。在分析计算中,暗物质部分是通过在可见部分增加一个U(1)-规范场来模拟的。反作用分析表明,暗涡的存在的影响是远远复杂的,而不仅仅是造成赤字的角度。涡旋引起能层移动,事件视界速度也受到涡旋的影响。这些现象比在可见的涡旋扇区的情况下更显著。一个黑洞的事件视界的面积减少,这种下降是更大的克尔黑洞与阿贝尔希格斯涡旋的情况相比。在分析了一般设置的引力性质之后,我们专注于粒子物理学激发的模型子集。我们保留了阿贝尔希格斯模型作为对暗物质扇区的描述(这个扇区包含一个重暗光子和一个额外的复标量),并增加了一个代表幺正规范中希格斯二重态实分量的实标量,以及一个额外的代表普通电磁场的U(1)-规范场。此外,我们考虑了两个耦合通道之间的可见和黑暗的部门,这是动力学混合的规范场和四次耦合之间的标量场。通过数值求解物质场的运动方程,我们分析了宇宙弦在暗物质扇区中的性质及其对直接耦合到它的可见扇区场的影响,发现宇宙弦的存在引起了Higgs场真空期望值的空间变化和黑洞周围的非零电磁场。

英文摘要:

We examined analytically and proposed a numerical model of an Abelian Higgs dark matter vortex in the spacetime of a stationary axisymmetric Kerr black hole. In analytical calculations the dark matter sector was modeled by an addition of a U (1)-gauge field coupled to the visible sector. The backreaction analysis revealed that the impact of the dark vortex presence is far more complicated than causing only a deficit angle. The vortex causes an ergosphere shift and the event horizon velocity is also influenced by its presence. These phenomena are more significant than in the case of a visible vortex sector. The area of the event horizon of a black hole is diminished and this decline is larger in comparison to the Kerr black hole with an Abelian Higgs vortex case. After analyzing the gravitational properties for the general setup, we focused on the subset of models that are motivated by particle physics. We retained the Abelian Higgs model as a description of the dark matter sector (this sector contained a heavy dark photon and an additional complex scalar) and added a real scalar representing the real component of the Higgs doublet in the unitary gauge, as well as an additional U (1)-gauge field representing an ordinary electromagnetic field. Moreover, we considered two coupling channels between the visible and dark sectors, which were the kinetic mixing between the gauge fields and a quartic coupling between the scalar fields. After solving the equations of motion for the matter fields numerically we analyzed properties of the cosmic string in the dark matter sector and its influence on the visible sector fields that are directly coupled to it. We found out that the presence of the cosmic string induced spatial variation in the vacuum expectation value of the Higgs field and a nonzero electromagnetic field around the black hole.

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