Exploring the critical phenomena in gravitational collapse


Natural systems are generally complex owing to the interactions between the parts thus sometimes causing intriguing critical phenomena and discrete scale invariance. Choptuik pioneered the critical phenomena in gravitational collapse in the late twentieth century. His work based on simulating critical collapse of a massless scalar field in spherical symmetry in general relativity paved the way for subsequent studies in other symmetries, gravitational theories, and matter fields. Weak and strong scalar fields collapse and form a flat spacetime and black hole respectively, while critical collapse is the watershed of the two circumstances. The dynamics of critical collapse has exhibited interesting behaviors including mass scaling law, discrete self-similarities of the solution and universality.

Presently, numerical methods are widely used in the studies of critical collapse. However, analytical approaches are indispensable for looking deep into the nature of critical collapse. Unfortunately, the complexity of the Einstein equations has remained a great challenge in the development of analytical models. As such, the nature of critical collapse has not been fully understood.

In a research paper published in the journal, The European Physical Journal C, Dr. Jun-Qi Guo and Prof. Hongsheng Zhang from the University of Jinan presented a combination of numerical simulations and asymptotic analysis to explore the dynamics of critical collapse.

Briefly, the research team first cross-examined the results presented in the existing literature. Next, the authors observed that in spherical scalar collapse, the spacetime near the center is almost conformally flat. In addition, using a typical log-periodic formula in discrete scale invariance systems, they obtained first approximate analytic expression for the spacetime near the center.

The critical collapse was connected to the results on the dynamics near spacetime singularities derived from the literature: the Belinskii, Khalatnikov, and Lifshitz (BKL) conjecture and black hole formation. This is attributed to the fact that critical collapse ends with a naked singularity. It was found that critical collapse and black hole formation share some common features in the expressions for the spacetime and scalar field. However, not as in black hole formation, the dynamics near the naked singularity formed in critical collapse is not described by the Kasner solution. Consequently, the BKL conjecture does not hold. Such a difference was interpreted by the fact that scalar field and gravity in critical collapse are weaker than in black hole formation.

According to the authors, critical collapse comprises of gravity and reflections that compete and compromise each other at the center. These mechanisms have also been observed in many other complex systems. This picture may lead to further examination on the relationship between critical collapse and complex science.

In summary, Guo and Zhang successfully presented a critical study on the dynamics of critical collapse based on numerical simulations and asymptotic analysis. Being an intermediary subject connecting gravitation, complex systems and partial differential equations, further studies in critical collapse can enrich all these fields.

Exploring the critical phenomena in gravitational collapse - Advances in Engineering
Numerical results vs. approximate analytic expression for the metric near the center in critical collapse

Exploring the critical phenomena in gravitational collapse - Advances in Engineering

About the author

Dr. Jun-Qi Guo is a lecturer at the University of Jinan. He received his BSc, MSc, MA and PhD degrees from Yantai Normal University (Now: Ludong University), Huazhong University of Science and Technology, the University of Mississippi and Simon Fraser University, respectively. He then worked as a postdoc at Tata Institute of Fundamental Research. In 2016, he joined the University of Jinan as a lecturer. He works on gravitational physics. His research interests include gravitational collapse, spacetime singularities and numerical relativity.

About the author

Prof. Hongsheng Zhang received his PhD from the Institute of Theoretical Physics, Chinese Academy of Sciences in 2005, majored in theoretical physics. His research areas include gravitation and cosmology. He joined the University of Jinan in 2016.


Guo, J.-Q., & Zhang, H. (2019). Dynamics of critical collapse. The European Physical Journal C, 79, 625.

Go To The European Physical Journal C

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