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arXiv 1604.04718gr-qchep-th
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标量场作为耦合动力学物质-几何系统的内禀时间测度。II。带电引力坍缩

Scalar field as an intrinsic time measure in coupled dynamical matter-geometry systems. II. Electrically charged gravitational collapse

Anna Nakonieczna, Dong-han Yeom

摘要:

研究引力系统的动力学,特别是在量子引力体系中,提出了一个在演化过程中测量时间的问题。解决这个问题的方法之一是使用内部自由度之一作为时间变量。我们的研究的目的是检查是否一个标量场或任何其他动力学量的一部分,耦合的多组分物质几何系统可以被视为一个“时钟”在其演变过程中。利用2+2形式研究了Einstein和Brans-Dicke理论中自引力带电标量场的坍缩.我们的发现集中在出现奇点附近的高曲率时空区域,这是量子引力应用的关键。我们研究了Brans-Dicke耦合常数的几种取值以及Brans-Dicke与带电标量场之间的耦合。结果证明,演化的标量场和一个测量给定半径的球体内电荷量的函数都可以用来量化动力学时空部分中奇点附近的时间,其中奇点周围的视视界是类空的。在这方面,只有当两个场都存在于系统中,而且它们相互耦合时,才有可能在渐近时空区域中使用它们。麦克斯韦场四势的唯一非零分量不能用来量化整个中心奇点附近所考虑的过程中的时间。没有一个被研究的动力学量是测量柯西视界附近时间的好的候选者,柯西视界由于质量膨胀现象也是奇异的。

英文摘要:

Investigating the dynamics of gravitational systems, especially in the regime of quantum gravity, poses a problem of measuring time during the evolution. One of the approaches to this issue is using one of the internal degrees of freedom as a time variable. The objective of our research was to check whether a scalar field or any other dynamical quantity being a part of a coupled multi-component matter-geometry system can be treated as a `clock' during its evolution. We investigated a collapse of a self-gravitating electrically charged scalar field in the Einstein and Brans-Dicke theories using the 2+2 formalism. Our findings concentrated on the spacetime region of high curvature existing in the vicinity of the emerging singularity, which is essential for the quantum gravity applications. We investigated several values of the Brans-Dicke coupling constant and the coupling between the Brans-Dicke and the electrically charged scalar fields. It turned out that both evolving scalar fields and a function which measures the amount of electric charge within a sphere of a given radius can be used to quantify time nearby the singularity in the dynamical spacetime part, in which the apparent horizon surrounding the singularity is spacelike. Using them in this respect in the asymptotic spacetime region is possible only when both fields are present in the system and, moreover, they are coupled to each other. The only nonzero component of the Maxwell field four-potential cannot be used to quantify time during the considered process in the neighborhood of the whole central singularity. None of the investigated dynamical quantities is a good candidate for measuring time nearby the Cauchy horizon, which is also singular due to the mass inflation phenomenon.

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