Abstract
We study the spherical collapse of an over-density of a barotropic fluid with linear equation of state in a cosmological background. Fully relativistic simulations are performed by using the Baumgarte–Shibata–Shapiro–Nakamura formalism jointly with the Valencia formulation of the hydrodynamics. This permits us to test the universality of the critical collapse with respect to the matter type by considering the constant equation of state parameter ω as a control parameter. We exhibit, for a fixed radial profile of the energy-density contrast, the existence of a critical value ω ∗ for the equation of state parameter under which the fluctuation collapses to a black hole and above which it is diluting. It is shown numerically that the mass of the formed black hole, for subcritical solutions, obeys a scaling law M∝ | ω- ω ∗| γ with a critical exponent γ independent on the matter type, revealing the universality. This universal scaling law is shown to be verified in the empty Minkoswki and de Sitter space-times. For the full matter Einstein-de Sitter universe, the universality is not observed if conformally flat sub-horizon initial conditions are used. But when super-horizon initial conditions computed from the long-wavelength approximation are used, the universality appears to be true.
Original language | English |
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Article number | 38 |
Journal | General Relativity and Gravitation |
Volume | 53 |
Issue number | 4 |
DOIs | |
Publication status | Published - Apr 2021 |
Funding
Funding was provided by Fonds De La Recherche Scientifique - FNRS (Grant No. FC 17573) and European Research Council (Grant No. 670874) The authors warmly thanks Dr. I. Cordero-Carrión for helpful advices and discussions concerning the Valencia formulation and the numerical methods used in this work. F. S. is supported by a FRS-FNRS (Belgian Funds for Scientific Research) Research Fellowship. J.R. is supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Advanced Grant agreement No. 670874). This research used resources of the “Plateforme Technologique de Calcul Intensif (PTCI)” ( http://www.ptci.unamur.be ) located at the University of Namur, Belgium, which is supported by the F.R.S.-FNRS under the convention No. 2.5020.11. The PTCI is member of the “Consortium des Équipements de Calcul Intensif (CÉCI)” ( http://www.ceci-hpc.be ).
Funders | Funder number |
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Horizon 2020 Framework Programme | 670874 |
European Research Council | |
Fonds De La Recherche Scientifique - FNRS | FC 17573, 2.5020.11 |
Keywords
- BSSN
- Critical phenomena
- Numerical relativity
- Relativistic hydrodynamics
- Spherical collapse