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Geometrical origin for the compaction function for primordial black hole formation
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Geometrical origin for the compaction function for primordial black hole formation
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We propose a geometrical origin for the Shibata-Sasaki compaction function, which is known to be a reliable indicator of primordial black hole formation at least during radiation domination. In the long-wavelength limit, we identify it with a compactness function in the static spacetime obtained by removing the cosmological scale factor from the metric and this explains why it cannot be greater than $1/2$. If its maximum is below $1/2$, the perturbation is of type I. If its maximum equals $1/2$, it corresponds to an extremal surface, which is simultaneously a bifurcating trapping horizon and admits a circular photon orbit in the static spacetime. In the long-wavelength regime of the physical expanding Universe, the Shibata-Sasaki compaction reaches its maximum value of $1/2$ at maximal and minimal surfaces on the constant time spacelike hypersurface, which feature a type II perturbation and both correspond to photon spheres expanding along with the cosmological expansion. Thus, the Shibata-Sasaki compaction measures how close to the type II configuration the perturbed region is.
Forward citations
Cited by 4 Pith papers
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Compaction function in stochastic inflation: a \texttt{FOREST} of type I and II primordial black holes
Stochastic binary tree method computes compaction function in inflation to distinguish type I/II PBH fluctuations, finding broader mass distributions and type-II dominance in quantum regimes of a toy model.
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Nonlinear long-wavelength solutions are constructed for cosmological perturbations in non-adiabatic multi-fluid systems, admitting adiabatic and entropy modes at leading order via ADM and gradient expansion.
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Friction in Stochastic Inflation
Adding a constant drift to time-reversed stochastic inflation in a flat potential yields an exact curvature distribution with exponential tails; forward and reverse delta-N formalisms differ by a factor of two in the ...
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Primordial Black Holes: A Review of Formation and Evolution
Review of PBH formation via compaction function and relativistic thresholds in FLRW backgrounds, arguing that memory burden and curvature corrections halt evaporation to leave Planck-scale relics.
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