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arXiv 1609.02556astro-ph.COgr-qchep-th
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收缩宇宙中的黑洞形成

Black hole formation in a contracting universe

Jerome Quintin, Robert H. Brandenberger

摘要:

我们研究收缩宇宙中宇宙学扰动的演化。我们的目标是确定在什么条件下密度扰动增长,形成大的不均匀性和坍缩成黑洞。我们的方法包括在解决宇宙学扰动方程的完全一般性的流体动力学流体。然后,我们描述了在不同的感兴趣的长度尺度上的波动的演化,并作为流体状态方程的函数,我们探索了两种不同类型的初始条件:量子真空和热波动。我们还导出了亚哈勃尺度下黑洞坍缩的一般条件,并利用Press-Schechter形式描述了黑洞的形成概率.对于具有小声速的流体(例如,尘埃),我们发现量子和热初始涨落都在收缩的宇宙中增长,最大的不均匀性首先坍缩成黑洞是哈勃大小的,坍缩发生在达到普朗克尺度之前。对于辐射主导的流体,我们发现在达到普朗克尺度之前,没有黑洞可以形成。因此,在物质反弹宇宙学的背景下,似乎只有在宇宙演化早期开始辐射主导时代的模型才能对黑洞的形成具有鲁棒性。然而,黑洞的形成可能是其他模型的一个有趣特征。我们评论了一些可能的替代早期宇宙的情况下,可以利用这一功能。

英文摘要:

We study the evolution of cosmological perturbations in a contracting universe. We aim to determine under which conditions density perturbations grow to form large inhomogeneities and collapse into black holes. Our method consists in solving the cosmological perturbation equations in complete generality for a hydrodynamical fluid. We then describe the evolution of the fluctuations over the different length scales of interest and as a function of the equation of state for the fluid, and we explore two different types of initial conditions: quantum vacuum and thermal fluctuations. We also derive a general requirement for black hole collapse on sub-Hubble scales, and we use the Press-Schechter formalism to describe the black hole formation probability. For a fluid with a small sound speed (e.g., dust), we find that both quantum and thermal initial fluctuations grow in a contracting universe, and the largest inhomogeneities that first collapse into black holes are of Hubble size and the collapse occurs well before reaching the Planck scale. For a radiation-dominated fluid, we find that no black hole can form before reaching the Planck scale. In the context of matter bounce cosmology, it thus appears that only models in which a radiation-dominated era begins early in the cosmological evolution are robust against the formation of black holes. Yet, the formation of black holes might be an interesting feature for other models. We comment on a number of possible alternative early universe scenarios that could take advantage of this feature.

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