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arXiv 1012.4369astro-ph.COgr-qchep-th
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分离的宇宙不限制原始黑洞的形成

Separate Universes Do Not Constrain Primordial Black Hole Formation

Michael Kopp, Stefan Hofmann, Jochen Weller

摘要:

卡尔和霍金证明了被平坦的FRW宇宙包围的球形过密区域的适当大小不可能是任意大的,否则该区域会自我封闭并成为一个独立的宇宙。从这个结果中,他们得出了一个连接过密区域的大小和密度的条件,确保它是我们宇宙的一部分。卡尔利用这个条件得到了密度波动幅度的上限,并得出了这样的结论:对于较小的幅度,原始黑洞的形成是可能的,而较大的幅度则表明存在一个独立的宇宙。相比之下,我们发现,最大值的出现并不是避免分离宇宙的结果,而是自然产生于所选切片的几何形状。用一个体积涨落变量代替密度揭示了涨落是一个独立的宇宙当且仅当这个变量在超视界尺度上发散。因此,卡尔和霍金的条件并没有对密度涨落造成物理约束。原始黑洞形成的初始曲率波动幅度大于对应的最大密度波动幅度的动力学以前没有被详细考虑,所以我们比较它的振幅较小的著名的情况下,通过提出嵌入和共形图的两种类型的尘埃时空。

英文摘要:

Carr and Hawking showed that the proper size of a spherical overdense region surrounded by a flat FRW universe cannot be arbitrarily large as otherwise the region would close up on itself and become a separate universe. From this result they derived a condition connecting size and density of the overdense region ensuring that it is part of our universe. Carr used this condition to obtain an upper bound for the density fluctuation amplitude with the property that for smaller amplitudes the formation of a primordial black hole is possible, while larger ones indicate a separate universe. In contrast, we find that the appearance of a maximum is not a consequence of avoiding separate universes but arises naturally from the geometry of the chosen slicing. Using instead of density a volume fluctuation variable reveals that a fluctuation is a separate universe iff this variable diverges on superhorizon scales. Hence Carr's and Hawking's condition does not pose a physical constraint on density fluctuations. The dynamics of primordial black hole formation with an initial curvature fluctuation amplitude larger than the one corresponding to the maximum density fluctuation amplitude was previously not considered in detail and so we compare it to the well-known case where the amplitude is smaller by presenting embedding and conformal diagrams of both types in dust spacetimes.

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