https://doi.org/10.1140/epjc/s10052-024-12564-5
Regular Article - Theoretical Physics
Non-singular gravitational collapse through modified Heisenberg algebra
1
Department of Physics, “Sapienza” University of Rome, P.le Aldo Moro, 5, 00185, Rome, Italy
2
INFN, Sezione di Roma1, P.le A. Moro 2, 00185, Rome, Italy
3
ENEA, Fusion and Nuclear Safety Department, C.R. Frascati, Via E. Fermi, 45, 00044, Frascati, RM, Italy
Received:
10
January
2024
Accepted:
14
February
2024
Published online:
12
March
2024
We study the effects of cut-off physics, in the form of a modified algebra inspired by Polymer Quantum Mechanics and by the Generalized Uncertainty Principle representation, on the collapse of a spherical dust cloud. We analyze both the Newtonian formulation, originally developed by Hunter, and the general relativistic formulation, that is the Oppenheimer–Snyder model; in both frameworks we find that the collapse is stabilized to an asymptotically static state above the horizon, and the singularity is removed. In the Newtonian case, by requiring the Newtonian approximation to be valid, we find lower bounds of the order of unity (in Planck units) for the deformation parameter of the modified algebra. We then study the behaviour of small perturbations on the non-singular collapsing backgrounds, and find that for certain range of the parameters (the polytropic index for the Newtonian case and the sound velocity in the relativistic setting) the collapse is stable to perturbations of all scales, and the non-singular super-Schwarzschild configurations have physical meaning.
The original online version of this article was revised to correct five incorrect DOIs in the bibliography. The corrected references are: [10] https://doi.org/10.1051/0004-6361/201220986, [14] https://doi.org/10.1103/PhysRevD.54.1474, [15] https://doi.org/10.1103/PhysRevD.96.084019, [16] https://doi.org/10.1103/PhysRevD.100.124013, [52] https://doi.org/10.1103/PhysRevD.104.064020.
An erratum to this article is available online at https://doi.org/10.1140/epjc/s10052-024-13157-y.
Copyright comment corrected publication 2024
© The Author(s) 2024. corrected publication 2024
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