Helical symmetry in general relativity

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Written by Martin Scholtz

In the flat spacetime, helically symmetric solutions represent particles moving periodically along the closed orbits, e.g. two particles orbiting about their common centre of mass. Such solutions exist in Maxwell's theory or in the scalar gravity, where the energy loss by radiation is compensated by introducing the advanced potentials. However, there are fundamental obstacles in defining the notion of helical symmetry in the context of full general relativity, although such solutions are believed to play an important role in numerical simulations of the binary inspiral. In this talk, we present 2-particle helically symmetric solution of linearized Einstein's equations and discuss some of its properties: conditions of equilibrium, asymptotic behaviour and peeling properties of the Weyl tensor and geodesics in helically symmetric spacetimes.