Particlelike solutions of the Einstein-Dirac equations
Particlelike solutions of the Einstein-Dirac equations
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爱因斯坦-狄拉克方程的粒子状解
DOI：
10.1103/physrevd.59.104020
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发表时间：
1998
影响因子：
5
通讯作者：
S. Yau
中科院分区：
文献类型：
--
作者：
F. Finster;J. Smoller;S. Yau
导出了具有单重态的两个费米子的静态球对称系统的耦合爱因斯坦-狄拉克方程。利用数值方法，我们构造了这些方程的无穷多个类孤子解。分析了溶液的稳定性。对于弱耦合（即费米子的静止质量小），所有的解都是线性稳定的（相对于球对称扰动），而对于强耦合，稳定和不稳定的解都存在。对于物理解释，我们讨论了费米子的能量和（ADM）质量如何作为费米子静止质量的函数。虽然引力是不可重整的，但我们的爱因斯坦-狄拉克方程的解是规则的，即使对于强耦合也是表现良好的。
The coupled Einstein-Dirac equations for a static, spherically symmetric system of two fermions in a singlet spinor state are derived. Using numerical methods, we construct an infinite number of soliton-like solutions of these equations. The stability of the solutions is analyzed. For weak coupling (i.e., small rest mass of the fermions), all the solutions are linearly stable (with respect to spherically symmetric perturbations), whereas for stronger coupling, both stable and unstable solutions exist. For the physical interpretation, we discuss how the energy of the fermions and the (ADM) mass behave as functions of the rest mass of the fermions. Although gravitation is not renormalizable, our solutions of the Einstein-Dirac equations are regular and well-behaved even for strong coupling.