08th July 2021

Featured Review

A Statistical Theory of Gravitating Body Formation in Extrasolar Systems

Reviewed by Sergei Eremenko

I am pleased to provide a short review of the book A Statistical Theory of Gravitating Body Formation in Extrasolar Systems by Professor A.M. Krot, whom I have known since the 1990s based on publications in common journals.

The author has been working on the statistical theory of gravitation for a few decades. This book is a life-long journey to understand and advance complex problems of gravity. These problems have been especially important since the ground-breaking discoveries of Einstein’s General Relativity (GR) in the 1920s. Even without Einstein, the problem of accounting for multiple bodies interacting with each other by Newton’s gravity law is complex enough due to the need to take into consideration the influence of the Newtonian forces of gravity of a group of bodies on another group of bodies.  As such, the problem needs to be understood in some statistical—rather than purely physical—sense. This is where ‘statistical gravity’ emerges. However, the problem becomes even more complex in General Relativity, which considers the forces ‘fictional’ and replaces them with the ‘curvature of space-time’. Even for a few bodies, the GR equations are overly complex, including nonlinear Ricci tensors, and accurately resolving highly nonlinear differential equations for the interaction of many bodies is a task of monumental complexity, even without applying statistical methods on top of this.

From the early works of the author from the 1990s, he has provided a unique mathematical approach to formulating the problem of gravity as a statistical phenomenon. This solid and systematic book contains a rigorous description of multiple theories, including the formation of matter from ‘molecular clouds’ and processes of ‘initial gravitational condensation’, among others. Especially interesting is the invitation of nonlinear Schrödinger quantum models typically used for describing solitonic wave-packets, seemingly applicable here in explaining the formation of a solitary body from surrounding matter clouds. In a ‘quantum’ sense, the formation of a massive body like a planet is considered as a process like a wave function concentration/collapse in quantum mechanics, with the hypothesis that quantum fluctuation effects and solitary matter condensation effects play a significant, if not major, role in the formation of stars, planets, and, ultimately, clusters of galaxies. This correlates well with the well-known hypothesis of the quantum nature of visible oscillations in a microwave background radiation, cosmological picture where tiny matter condensations evolved into galaxies and clusters over time.

In summary, the book looks solid, well-structured, and encompasses the life-long journey of the author to understand and advance the fascinating and still not well-understood world of cosmological formations around us, from the position of novel theories of statistical gravitations and nonlinear quantum models.

As a suggestion for further research, it would be interesting to develop a new theory of statistical quantum gravity where quantum mechanics, general relativity, and notable statistics would be combined into one theory. In addition, the author may consider publishing a new popularisation book on the matter understood by the general public and students.

Sydney, Australia, 2021.


Sergei Eremenko is an Australian, Ukrainian born scientist, author of three books, formerly one of the youngest Professors in the world, Doctor of Engineering, PhD, Honorary Professor and 'rocket scientist' graduated from National Aerospace University of Ukraine.


A Statistical Theory of Gravitating Body Formation in Extrasolar Systems is available now in Hardback at a 25% discount. Enter the code PROMO25 at the checkout to redeem.

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