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Revisiting compaction functions for primordial black hole formation
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Shibata and Sasaki [arXiv:gr-qc/9905064] introduced the so-called compaction function. Since then, it has been empirically established that the maximum value of this function (or its volume-averaged counterpart) in the long-wavelength solutions gives a very robust threshold of primordial black hole formation. In this paper, we show that in spite of initial intention, the Shibata-Sasaki compaction function cannot be interpreted as the ratio of the mass excess to the areal radius in the constant-mean-curvature slice of their choice but coincides with that in the {\it comoving} slice up to a constant factor depending on the equation of state. We also discuss the gauge-(in)dependence of the legitimate compaction function, i.e., the ratio of the mass excess to the areal radius, in the long-wavelength solutions.
Forward citations
Cited by 3 Pith papers
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The statistics of curvature-profile dispersion in primordial black hole formation
Rare coherent shape deformations of primordial curvature profiles can dominate primordial black hole abundance by lowering the collapse threshold enough to overcome their Gaussian statistical cost.
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Curvature Perturbations from First-Order Phase Transitions: Implications to Black Holes and Gravitational Waves
Covariant analysis of curvature perturbations from first-order phase transitions reveals gauge-dependent overestimation of primordial black holes and gravitational waves in prior non-covariant calculations, leading to...
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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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