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arXiv 2112.04065gr-qc
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非最小耦合标量场的临界引力坍缩

Critical gravitational collapse of a non-minimally coupled scalar field

Erik Jiménez-Vázquez, Miguel Alcubierre

摘要:

利用一个带强度参数$ξ$的二次耦合函数,研究了与引力非极小耦合的无质量标量场的临界引力坍缩。我们专注于临界现象的类型II,并确定与至少$10^{-12}$的准确性的临界振幅的值崩溃到一个黑洞,以及临界和回声指数的值。在临界振幅中获得如此高的精度要求我们进行坐标径向变换,该变换有效地将中心区域附近的分辨率提高至少$10^3$的因子。正如预期的那样,我们发现,对于小耦合的情况下的临界行为是非常相似的最小耦合标量场。另一方面,对于高耦合,动力学变得如此剧烈,以至于我们需要引入一个特殊的切片条件,称为激波避免切片条件,以避免规范病理,否则会导致我们的模拟失败。有了这个新的规范条件,我们能够进行高精度的模拟,即使在强耦合制度,在那里我们发现,临界和回声指数变得显着更小,和回声行为更丰富,不能用一个单一的谐波建模。

英文摘要:

We study the critical gravitational collapse of a massless scalar field non-minimally coupled to gravity, using a quadratic coupling function with a strength parameter $ξ$. We concentrate on critical phenomena of type II, and determine with an accuracy of at least $10^{-12}$ the value of the critical amplitude for collapse to a black hole, as well as the values of the critical and echoing exponents. Obtaining such high accuracy in the critical amplitude requires us to do a coordinate radial transformation that effectively increases resolution near the central regions by a factor of at least $10^3$. As expected, we find that for the case of small coupling the critical behaviour is very similar to that of a minimally coupled scalar field. On the other hand, for high coupling the dynamics become so violent that we need to introduce a special slicing condition, known as the shock-avoiding slicing condition, in order to avoid gauge pathologies that would otherwise cause our simulations to fail. With this new gauge condition we are able to perform high accuracy simulations even in the strong coupling regime, where we find that the critical and echoing exponents become significantly smaller, and that the echoing behavior is richer and can not be modelled by a single harmonic.

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。

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