Turning Point Principle for Relativistic Stars
Turning Point Principle for Relativistic Stars
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DOI：
10.1007/s00220-021-04197-6
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发表时间：
2021-09-12
影响因子：
2.4
通讯作者：
Lin, Zhiwu
中科院分区：
文献类型：
--
作者：
Hadzic, Mahir;Lin, Zhiwu
指定状态方程后，爱因斯坦-欧拉系统的球对称稳态被嵌入到 1 参数解族中，其特征在于其中心红移值。在 1960 年代，Zel'dovich (Voprosy Kosmogonii 9:157-170, 1963) 和 Harrison 等人。 （引力理论和引力塌缩。芝加哥大学出版社，芝加哥，1965）提出了一个转折点原理，该原理指出，只有在沿质量半径曲线的质量极值处，谱稳定性才能转变为不稳定，反之亦然。此外，极值处的弯曲方向决定了生长模式是获得还是丢失。我们证明了转折点原理并提供了线性化动力学的详细描述。我们的结果的推论之一是，随着中心红移增加到无穷大，生长模式的数量也会增加到无穷大。
Upon specifying an equation of state, spherically symmetric steady states of the Einstein-Euler system are embedded in 1-parameter families of solutions, characterized by the value of their central redshift. In the 1960's Zel'dovich (Voprosy Kosmogonii 9:157-170, 1963) and Harrison et al. (Gravitation Theory and Gravitational Collapse. The University of Chicago press, Chicago, 1965) formulated a turning point principle which states that the spectral stability can be exchanged to instability and vice versa only at the extrema of mass along the mass-radius curve. Moreover the bending orientation at the extrema determines whether a growing mode is gained or lost. We prove the turning point principle and provide a detailed description of the linearized dynamics. One of the corollaries of our result is that the number of growing modes grows to infinity as the central redshift increases to infinity.