Primordial black holes in linear and non-linear regimes

Understand

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.