Imposing a "Traffic Law" on Spacetime Curvature

Dr. Andrei Frolov from the Department of Physics at Simon Fraser University and Dr. Valeri Frolov from the Theoretical Physics Institute at the University of Alberta co-published a paper which became the title story on the journal MDPI Universe.

Classical mechanics and general relativity are two cornerstones of the modern physics. But what would happen if they obeyed traffic laws, like a speed limit? Researchers from Simon Fraser University and University of Alberta set out to explore this question, with results making the cover of MDPI Universe, where the article was published.

Einstein’s theory of gravity is a remarkable theory which explains all known observations in astrophysics and cosmology. However, it is incomplete and predicts inevitable singularities both inside black holes and in cosmology. Close to such a singularity the spacetime curvature grows infinitely, and according to general relativity the spacetime simply terminates its existence. There were a lot of attempts to resolve this problem by modifying the equations in the very high energy domain. It is believed that the spacetime could again be described by the Einstein's theory after passing this "dangerous" (high curvature) region. How does the spacetime do it and how its properties before and after this regime are related? At the moment we do not know the answer to those questions. In the absence of reliable theory describing details of this process, one can try to attack the problem by simply imposing a "traffic law" on the curvature. Namely, one could assume that when the curvature reaches some limiting value, it does not grow further and remains constant. Such an assumption imposes an inequality constraint on the evolution. In this paper the authors developed a general approach which allows one to study a wide class of dynamical systems with inequality constraints. They explain general properties of such systems and describe their application to black holes and cosmology.