The Ehlers-Kundt conjecture about gravitational waves and dynamical systems

摘要: Abstract The Ehlers-Kundt conjecture is a physical assertion about the fundamental role of plane waves for description gravitational waves. Mathematically, it becomes equivalent to problem on Euclidean R 2 with very simple formulation in Classical Mechanics: given non-necessarily autonomous potential V ( z , u ) ∈ × harmonic (i.e. source-free), trajectories its associated dynamical system ¨ s = − ∇ are complete (they live eternally) if and only polynomial degree at most (so that standard mathematical idealization vacuum). Here, solved significant case bounded polynomially intervals. implications this EK conjecture, as well non-polynomial one, discussed beyond their original scope.