arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2108.02841gr-qc
收藏

Newman-Janis旋转系统的物理解释。II。总体系

Physical interpretation of Newman-Janis rotating systems. II. General systems

Philip Beltracchi, Paolo Gondolo

摘要:

德雷克和塞凯雷斯扩展了纽曼-詹尼斯算法,从爱因斯坦方程的一般静态球对称解产生静态轴对称时空。该算法在数学上生成旋转解的能量-动量张量,但旋转和非旋转系统可能代表也可能不代表相同的物理系统,在两者都是理想流体、电磁场或$Λ$项等意义上。(arxiv:2104.02255),我们比较了旋转和非旋转能量动量张量的本征值和本征向量的结构(他们的Segre类型),并寻找与Kerr-Schild系统的旋转能量密度和主压有关的状态方程的存在性。在这里,我们将我们的分析扩展到一般静态球对称系统根据Drake-Szekeres推广的Newman-Janis算法。我们发现这些旋转系统除了[31]和[(31)]之外几乎可以有所有的Segre型。此外,时空的塞格雷型在从非旋转到旋转的过程中会发生严重的变化,例如从最初的[(111,1)]种子系统到$[11Z\bar{Z}]$。我们还发现条件,规定有多少状态方程可能存在于一个德雷克Szekeres系统。

英文摘要:

Drake and Szekeres have extended the Newman-Janis algorithm to produce stationary axisymmetric spacetimes from general static spherically symmetric solutions of the Einstein equations. The algorithm mathematically generates an energy-momentum tensor for the rotating solution, but the rotating and nonrotating system may or may not represent the same physical system, in the sense of both being a perfect fluid, or an electromagnetic field, or a $Λ$-term, and so on. In Part I (arxiv:2104.02255), we compared the structure of the eigenvalues and eigenvectors of the rotating and nonrotating energy-momentum tensors (their Segre types) and looked for the existence of equations of state relating the rotating energy density and principal pressures for Kerr-Schild systems. Here we extend our analysis to general static spherically symmetric systems obtained according to the Drake-Szekeres generalization of the Newman-Janis algorithm. We find that these rotating systems can have almost all Segre types except [31] and [(31)]. Moreover, the Segre type of the spacetime can change severely in passing from the nonrotating to the rotating configurations, for example to $[11Z\bar{Z}]$ from seed systems which were initially [(111,1)]. We also find conditions dictating how many equations of state may exist in a Drake-Szekeres system.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑