Strength of the naked singularity in critical collapse
School of Physics and Technology, University of Jinan, 250022, Jinan, Shandong, China
2 College of Mathematics and Statistics, Chongqing University, 401331, Chongqing, China
3 Institute of Applied Mathematics, Morningside Center of Mathematics and LESC, Institute of Computational Mathematics, Academy of Mathematics and System Science, Chinese Academy of Sciences, University of Chinese Academy of Sciences, 100190, Beijing, China
4 International Center for Cosmology, Charusat University, 388421, Anand, Gujarat, India
Accepted: 16 September 2020
Published online: 7 October 2020
The critical collapse of a scalar field is a threshold solution of black hole formation, in which a naked singularity arises. We study here the curvature strength of this singularity using a numerical ansatz. The behavior of the Jacobi volume forms is examined along a non-spacelike geodesic in the limit of approach to the singularity. These are seen to be vanishing, thus showing that all physical objects will be crushed to zero size near the singularity. Consequently, although the critical collapse is considered to be a fine-tuning problem, the naked singularity forming is gravitationally strong. This implies that the spacetime cannot be extended beyond the singularity, thus making the singularity genuine and physically interesting. These results imply that the nature of critical collapse may need to be examined and explored further.
© The Author(s) 2020
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