Dynamical solutions for an evolving multiple network of black holes near a cosmological bounce dominated by a scalar field are investigated. In particular, we consider the class of black hole lattice models in a hyperspherical cosmology, and we focus on the special case of eight regularly-spaced black holes with equal masses when the model parameter κ > 1. We first derive exact time evolving solutions of instantaneously-static models, by utilizing perturbative solutions of the constraint equations that can then be used to develop exact 4D dynamical solutions of the Einstein field equations. We use the notion of a geometric horizon, which can be characterized by curvature invariants, to determine the black hole horizon. We explicitly compute the invariants for the exact dynamical models obtained. As an application, we discuss whether black holes can persist in such a Universe that collapses and then subsequently bounces into a new expansionary phase. We find evidence that in the physical models under investigation (and particularly for κ > 1) the individual black holes do not merge before nor at the bounce, so that consequently black holes can indeed persist through the bounce.

中文翻译：

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黑洞晶格宇宙学模型中的持久性

研究了在标量场主导的宇宙反弹附近不断演化的多重黑洞网络的动力学解决方案。特别地，我们考虑了超球面宇宙学中的黑洞晶格模型类，并且我们专注于当模型参数 κ > 1 时具有相同质量的八个规则间隔黑洞的特殊情况。我们首先推导出精确的时间演化解瞬时静态模型，通过利用约束方程的微扰解，然后可用于开发爱因斯坦场方程的精确 4D 动力学解。我们使用几何视界的概念，可以用曲率不变量来表征，来确定黑洞视界。我们明确地计算获得的精确动力学模型的不变量。作为应用程序，我们讨论了黑洞是否可以在这样一个崩溃的宇宙中持续存在，然后又反弹到一个新的膨胀阶段。我们发现证据表明，在所研究的物理模型中（尤其是对于 κ > 1），单个黑洞在反弹之前和反弹时都不会合并，因此黑洞确实可以在反弹过程中持续存在。