Led by Maciej MALIBORSKI, opens an external URL in a new window, a new research project explores (quasi-) periodic solutions of the Einstein equations. The focus is on understanding how physical systems in which energy remains confined can generate wave patterns that repeat exactly or nearly exactly over time.

Using simplified mathematical models, the project investigates the mechanisms behind such persistent and stable oscillations. The aim is to develop methods that can later be applied to more realistic and complex systems—ultimately including the fundamental equations of general relativity.

This research is particularly challenging because the Einstein equations are highly complex, even in strongly simplified and symmetry-reduced settings. Progress therefore relies on a close interplay between rigorous analytical mathematics and precise numerical simulations. Recent results obtained from model problems already indicate that these recurring dynamics are far richer than previously thought, revealing new branches of solutions and intricate, sometimes fractal-like structures.

In the long term, the project will contribute to a deeper understanding of nonlinear oscillations in systems where energy is trapped. This is not only relevant for fundamental questions in gravitational physics but also broadens our knowledge of the underlying laws of nature. Moreover, the research fosters the development of new mathematical and computational methods with potential applications across a wide range of scientific fields.