Spin vector deviation and the gravitational wave memory effect between two free-falling gyroscopes in the plane wave spacetimes

Abstract

In plane wave spacetimes, we find that there will be a precession angle deviation between two free-falling gyroscopes when gravitational waves passed through. This kind of angle deviation is closely related to the well-known standard velocity memory effect. Initial conditions such as the separation velocity or displacement between the two gyroscopes will affect this angle deviation. This result might be understood as a special relativistic consequence of the velocity memory. The evolutions of the angle deviation are calculated for different cases. We find that in some extreme circumstances, the angle deviation's order of magnitude produced by a rotating compact binary source could be ${10}^{\ensuremath{-}14}\text{ }\text{ }\mathrm{rads}$. Therefore, this memory effect caused by the gravitational wave is likely to be detected in the future.