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Abstract We compute families of solutions to the Einstein vacuum equations of the type of Brill waves, but with slow fall-off towards spatial infinity. We prove existence and uniqueness of solutions for physical data and numerically construct some representative solutions. We numerically construct an explicit example with slow-off which does not exhibit antipodal symmetry at spatial infinity. 

Abstract We describe an experiment to measure the electromagnetic analog of gravitational wave memory, the so-called electromagnetic (EM) memory. Whereas gravitational wave memory is a residual displacement of test masses, EM memory is a residual velocity (i.e. kick) of test charges. The source of gravitational wave memory is energy that is not confined to any bounded spatial region: in the case of binary black hole mergers the emitted energy of gravitational radiation as well as the recoil energy of the final black hole. Similarly, EM memory requires a source whose charges are not confined to any bounded spatial region. While particle beams can provide unbounded charges, their currents are too small to be practical for such an experiment. Instead we propose a short microwave pulse applied to the center of a long dipole antenna. In this way the measurement of the kick can be done quickly enough that the finite size of the antenna does not come into play and it acts for our purposes the same as if it were an infinite antenna. 

Abstract In this article, we compare in detail the linear and nonlinear approach to the Gravitational Waves Displacement and Velocity Memory (GWDM and GWVM) effects. We consider astrophysical situations that give rise to gravitational waves with GWVM effect, i.e. with a residual velocity (the so-called ‘velocity-coded memory’) and discuss the possibility of future detection of the GWVM effect.