相对论恒星的隐形自发旋量化
Stealth spontaneous spinorization of relativistic stars
摘要：
我们研究了广义相对论高密度恒星背景中Dirac旋量场的行为以及类似于自发标量化的自发旋量化的可能性。我们考虑了通过引入第五伽玛矩阵${\hat γ}^5$来修正Dirac场动力学项的模型以及Dirac旋量场与物质扇区的共形耦合，这将导致Dirac旋量场在高密度致密恒星背景中的快子增长.为了得到静态解和球对称解，我们必须同时考虑两个狄拉克场。我们表明，在恒定密度的恒星背景下，我们的模型产生的狄拉克旋量场的非平凡的解决方案，任何数量的节点，其中一个模式有一个比其他更多的节点。我们还证明了在任意静态和球对称时空背景中，对于任意可分的狄拉克旋量场的含时无规，在首阶，狄拉克旋量场的有效能量动量张量的所有分量在两个场求和后都为零，这表明在具有任意节点数的静态和球对称时空中，自发旋量化作为一个隐形过程发生，其将被非线性效应猝灭并且不留下可观察的效应。
英文摘要：
We investigate the behavior of the Dirac spinor fields in general relativistic high density stellar backgrounds and the possibility of spontaneous spinorization which is analogous to spontaneous scalarization. We consider the model with the modified kinetic term of the Dirac field by the insertion of the fifth gamma matrix ${\hat γ}^5$ and the conformal coupling of the Dirac spinor field to the matter sector, which would lead to the tachyonic growth of the Dirac spinor field in the high density compact stellar backgrounds. In order to obtain the static and spherically symmetric solutions, we have to consider the two Dirac fields at the same time. We show that in the constant density stellar backgrounds our model gives rise to the nontrivial solutions of the Dirac spinor fields with any number of nodes, where one mode has one more nodes than the other. We also show that at the leading order all the components of the effective energy-momentum tensor of the Dirac spinor fields, after the summation over the two fields, vanish for any separable time-dependent ansatz of the Dirac spinor fields in any static and spherically symmetric spacetime backgrounds, indicating that spontaneous spinorization takes place as a stealth process in the static and spherically symmetric spacetime with any number of nodes, which would be quenched by nonlinear effects and leave no observable effects.
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