Revisiting compaction functions for primordial black hole formation
Abstract
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.
Keywords
Cite
@article{arxiv.2304.13284,
title = {Revisiting compaction functions for primordial black hole formation},
author = {Tomohiro Harada and Chul-Moon Yoo and Yasutaka Koga},
journal= {arXiv preprint arXiv:2304.13284},
year = {2023}
}
Comments
17 pages, minor correction, accepted for publication in Physical Review D