(Gravitational Wave) Memory of Starobinsky in a Time Crystal (Condensate)

Abstract

In this Letter we have revealed the presence of Gravitational Wave Memory Effect (GWME) in a new and physically appealing scenario - the Time Crystal (TC) condensate of Starobinsky Quadratic Gravity. We have used a Gravitational Wave form, induced in a TC condensate in FLRW spacetime, that is much more general than the idealized and somewhat unphysical Plane Wave spacetimes, that are conventionally used. We have presented new results for non-zero GWME, both in coordinate and in velocity variables. The results are expressed in Cartesian and Brinkmann coordinates. Approximate analytic forms of transverse geodesics in Brinkmann coordinates are provided. Very rough quantitative estimates for GWME are also suggested.