论文标题
在矢量场耦合到物质的情况下，自发矢量化
Spontaneous vectorization in the presence of vector field coupling to matter
论文作者
论文摘要
我们研究了与物质的矢量保形和异形耦合中自发矢量化的可能性。我们研究了相对论恒星的静态和球形对称解，其矢量场的非平地曲线满足边界条件的$a_μ\至0 $在空间无穷大，其中$a_μ$代表矢量场。首先，我们研究了有关一般相对论（GR）恒星解决方案的线性扰动，其消失了矢量场$a_μ= 0 $。我们表明，纯矢量失真耦合会导致GR恒星的幽灵或梯度不稳定性，这表明GR恒星背景上的双曲线分解。另一方面，纯条耦合会导致GR溶液的速度不稳定性，并将导致向量场的自发生长朝着非平凡溶液的自发生长，就像标量探测理论中自发标量的方式一样。然后，在存在纯粹的错误耦合的情况下，我们用相对论恒星的静态和球形对称解，售价为$ 0 $和$ 1 $的节点。我们发现，具有非平凡矢量场的溶液的性质与广义Proca理论相似。与Mass-Radius图中一样，$ 0 $和$ 1 $节点解决方案的分支与较低密度制度中的GR解决方案的分支相关，它们可能是根据初始条件的选定选择形成的。最后，我们在纯种保形耦合的情况下构建了$ 0 $节点溶液，并表明这些溶液的分支在低密度区域和高密度区域中都连接到GR溶液的分支，因此将通过GR溶液的连续演化自发出现。
We examine the possibility of spontaneous vectorization in the vector-tensor theories with the vector conformal and disformal couplings to matter. We study the static and spherically symmetric solutions of the relativistic stars with the nontrivial profile of the vector field satisfying the boundary conditions $A_μ\to 0$ at the spatial infinity, where $A_μ$ represents the vector field. First, we study the linear perturbations about the general relativistic (GR) stellar solutions with the vanishing vector field $A_μ=0$. We show that the pure vector disformal coupling causes the ghost or gradient instability of the GR stars, indicating the breakdown of the hyperbolicity on the GR stellar backgrounds. On the other hand, the pure conformal coupling causes the tachyonic instability of the GR solutions and would lead to the spontanenous growth of the vector field toward the nontrivial solutions as in the manner of spontaneous scalarization in the scalar-tensor theories. We then construct the static and spherically symmetric solutions of the relativistic stars with $0$ and $1$ nodes of the vector field in the presence of the pure disformal coupling. We find that the properties of the solutions with the nontrivial vector field are similar to those of the generalized Proca theories. As in the mass-radius diagram the branches of the $0$ and $1$ node solutions are disconnected to that of the GR solutions in the lower density regimes, they may be formed from the selected choice of the initial conditions. Finally, we construct the $0$ node solutions in the case of the pure conformal coupling, and show that the branch of these solutions is connected to that of the GR solutions in both the low and high density regions and hence would arise spontaneously via the continuous evolution from the GR solutions.
