arXiv 1608.005912016-08-01gr-qcastro-ph.CO

线性和非线性区域中的原始黑洞

Primordial black holes in linear and non-linear regimes

Alireza Allahyari, Javad T. Firouzjaee, Ali Akbar Abolhasani

备注：: 14 pages, 1 figure
DOI：: 10.1088/1475-7516/2017/06/041

摘要：

利用动态黑洞的视视界概念，我们重新讨论了线性和非线性两种情况下宇宙早期原初黑洞（PBH）的形成。首先，我们发展了球对称时空的微扰理论来研究线性区域中球形PBH的形成，并固定了两个规范。我们还引入了一个定义良好的规范不变量的扩展。使用这个量，我们认为PBH不形成的线性政权。最后，我们研究了非线性机制。在辐射占优时期，我们采用封闭的FRW模型来研究PBH的形成。从线性微扰理论出发，考虑到密度和速度的微扰，我们给出了球形坍缩的初始条件。我们的模型给出了一个约束的速度扰动。该模型还预测了当$δ> 3$ .应用声视界约束，我们已经证明视界再入时密度扰动的阈值必须大于$δ_{th} > 0.7$以克服压力梯度。

英文摘要：

Using the concept of apparent horizon for dynamical black holes, we revisit the formation of primordial black holes (PBH) in the early universe for both linear and non-linear regimes. First, we develop the perturbation theory for spherically symmetric spacetimes to study the formation of spherical PBHs in linear regime and we fix two gauges. We also introduce a well defined gauge invariant quantity for the expansion. Using this quantity, we argue that PBHs do not form in the linear regime. Finally, we study the non-linear regime. We adopt the spherical collapse picture by taking a closed FRW model in the radiation dominated era to investigate PBH formation. Taking the initial condition of the spherical collapse from the linear theory of perturbations, we allow for both density and velocity perturbations. Our model gives a constraint on the velocity perturbation. This model also predicts that the apparent horizon of PBHs forms when $δ> 3$. Applying the sound horizon constraint, we have shown the threshold value of density perturbations at horizon re-entry must be larger than $δ_{th} > 0.7$ to overcome the pressure gradients.

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