Primordial black holes in linear and non-linear regimes

Abstract

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 $\delta >3$. Applying the sound horizon constraint, we have shown the threshold value of density perturbations at horizon re-entry must be larger than ${\delta }_{th}>0.7$ to overcome the pressure gradients.

14 pages, 1 figure

References in corpus (5)

• Calculating the mass spectrum of primordial black holes
• Curvature profiles as initial conditions for primordial black hole formation
• Separate Universes Do Not Constrain Primordial Black Hole Formation
• The separate universe problem: 40 years on
• Cosmic Matter Flux May Turn Hawking Radiation Off

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• On the Merger Rate of Primordial Black Holes in Cosmic Voids
• Effect of a High-Precision Semi-Analytical Mass Function on the Merger Rate of Primordial Black Holes in Dark Matter Halos
• Point mass Cosmological Black Holes
• Extended primordial black hole mass functions with a spike
• Nonlinear phenomena in general relativity